Finite Difference - Science topic

We investigate Pareto equilibria for bi-objective optimal control problems. Our framework comprises the situation in which an agent acts with a distributed control in a portion of a given domain, and aims to achieve two distinct (possibly conflictive) targets. We analyze systems governed by linear and semilinear heat equations and also systems with...

This study aims to investigate and analyze the dynamics of diarrhea infectious disease model. For this purpose, a classical diarrhea disease model is converted into the diffusive diarrhea epidemic model by including the diffusion terms in every compartment of the system. Basic assumptions of the proposed model are described for a vivid understandin...

Buried pipelines are essential for the safe and efficient transportation of energy products such as oil, gas, and various chemical fluids. However, these pipelines are highly vulnerable to ground movements caused by geohazards such as seismic faults, landslide, liquefaction-induced lateral spreading, and soil creep, which can result in potential pi...

This study produces the solitary wave solutions to the modified equal‐width (MEW) model utilizing the He's semi‐inverse approach. This model is a generalization of the equal‐width (EW) equation, which is a nonlinear partial differential equation (NPDE) that describes wave propagation, particularly in shallow water waves. This model is also associat...

In recent years, the dipole shear wave in acoustic reflection logging has developed rapidly. The visualization of the radiation, reflection, and transmission wavefield of the dipole source in the formation is conducive to a more direct study of the wavefield characteristics of acoustic reflection imaging. To this end, based on the basic principle a...

In this research, a 1:4 D-multiplexer made of 2-D photonic crystal configurations is presented. Functionality of the proposed structure is studied by utilizing 2D finite difference time domain method. Proposed system is used as a sensitive 4 port biosensor for diagnosis of various biological elements (cholesterol, glucose, creatinine and hemoglobin...

In this paper, we develop efficient numerical methods and a general framework, based on AI technologies, to solve for financial derivatives prices and Greeks in a real-time manner. Our methodologies extend the traditional path derivative, likelihood ratio and finite difference approaches, making full use of machine learning techniques, and are able...

In this paper, we introduce a comprehensive computational framework to construct highly efficient linear energy stable methods for the incompressible Navier-Stokes equation, which preserve the original energy dissipation law. By multiplying the convection term by an identity-one term and incorporating a zero stabilization term, we recast the origin...

Uniformly approximating infinite-dimensional systems, such as those described by partial differential equations (PDEs), using infinitely many systems described by ordinary differential equations is crucial for their application in engineering. This paper examines uniform exponential stability for a semi-discrete scheme applied to a one-dimensional...

This dissertation focuses on a class of second-order two-parameter singularly perturbed parabolic problems, with and without time delay. These problems exhibit narrow boundary layers near the domain boundaries due to the presence of the perturbation parameters, as well as an interior layer because of the presence of the discontinuous data in the co...

In this paper we propose a structure-preserving, linearly implicit, second-order-in-time scheme for the numerical solution of the von Neumann equation with power nonlinearity (also known as the Alber equation). Fourth order finite differences are used for the spatial discretization. We highlight the importance of the correct initialization of the m...

This study investigates transport phenomena on two-dimensional, closed, regular manifolds governed by surface partial differential equations (SPDEs) of scalar hyperbolic conservation law (sHCL) type. A central focus is the formulation of the surface flux divergence to satisfy the geometry-compatible (GC) condition via a prescribed flux directional...

One of the critical factors in assessing the stability of tailings dams is the seepage field within the dam body. This study analyzed the spatial variability of the permeability coefficient on the Luomukeng tailings pond in Jiangxi, China and its effect on the seepage field. The research employed a heap dam model test, an internal permeability coef...

This research aims to better understand the fundamental behaviour of fluids by comparing the nature of a Newtonian fluid and Williamson fluid under the interaction of sinusoidal MHD fields, radiative heat flux of nanomaterial embedded in a porous stretched surface with accomplishments of Brownian motion, thermopho-resis, heat source, and chemical r...

The seventh-order boundary value problems (BVPs), which are important because of their complexity and prevalence in many scientific and engineering fields, are the subject of this paper’s study. These high-order boundary value problems appear in fields such as fluid dynamics, where they are used to model fluid flow, and in elasticity theory, where...

This paper investigates chaos control in the Sprott circuit, a minimal electronic system exhibiting complex nonlinear dynamics. Using the third-order nonlinear differential equation from Kaveh Merat paper, we model the circuit and implement delayed feedback control to suppress chaos. Experimental voltage data were extracted from published figures v...

Solving high-dimensional partial differential equations (PDEs) is an essential problem in various fields of science and engineering. Analytical solutions for high-dimensional PDEs are often intricate and rare, as very few problems possess such solutions. Therefore, numerical methods play a pivotal role in overcoming these challenges. This work prop...

In this paper, we propose a numerical method for the fractional Bagley–Torvik equation of variable coefficients with Robin boundary conditions. The problem is approximated using a finite difference scheme on a uniform mesh that combines the L1 scheme with central differences. We prove that this numerical method is almost first-order convergent. The...

We propose and analyze a Crank-Nicolson finite difference scheme for the (2+1)D regularized logarithmic nonlinear Schrödinger equation with general damping. The scheme is designed to preserve key structural properties of the continuous model and is shown to ensure the existence and uniqueness of the discrete solution, assuming the boundedness of di...

Deep State Space Models (SSMs) reignite physics-grounded compute paradigms, as RNNs could natively be embodied into dynamical systems. This calls for dedicated learning algorithms obeying to core physical principles, with efficient techniques to simulate these systems and guide their design. We propose Recurrent Hamiltonian Echo Learning (RHEL), an...

Surface enhanced Raman scattering (SERS) is a highly sensitive and precise technique that enables the acquisition of high-quality spectra from materials in tiny quantities, down to the single-molecule level. Today, this technique, with its high signal enhancement factor, is considered an efficient tool for molecular detection in biosensors. This ar...

In the article, we study an efficient numerical scheme to solve a class of space fractional Klein‐Gordon‐Schrödinger equations with periodic boundary condition. First, we propose finite difference scheme to discrete time derivative, and the space fractional derivative is approximated by Fourier spectral collocation method. Second, we prove that the...

A high-order physics-informed meshless finite difference numerical technique is introduced for solving the time-harmonic cold plasma wave equation in toroidal geometries, presenting a novel application of the generalized finite difference (GFD) method to plasma wave simulations. The algorithm employs an irregular distribution of computational point...

A review of five national standards for one-dimensional constant rate of displacement (CRD) consolidation tests reveals remarkable inconsistencies in the formulas used for determining the consolidation properties of soils under large deformations. The determination of finite-strain consolidation properties requires a large deformation consolidation...

Ultra-fast and highly compact optoelectronic devices are highly needed for optical communication systems. One of the primary devices used in such systems is the optical encoder. In this paper, we present a 4×2 encoder realized using a new photonic crystal (PhC) ring resonator design. The proposed encoder consists of four inputs, two outputs, and tw...

We consider a two-dimensional parabolic problem subject to both Neumann and Dirichlet boundary conditions, along with an integral constraint. Based on the integral observation, we solve the inverse problem of a recovering time-dependent right-hand side. By exploiting the structure of the boundary conditions, we reduce the original inverse problem t...

We introduce new Gaussian Process (GP) high-order approximations to linear operations that are frequently used in various numerical methods. Our method employs the kernel-based GP regression modeling, a non-parametric Bayesian approach to regression that operates on the probability distribution over all admissible functions that fit observed data....

We develop a comprehensive operator-based formalism for representing a wide range of statistical transformations using the Matrix Convolutional Theory (MCT) framework. This paper focuses on unifying continuous-time and discrete-time domains by expressing statistical operations-such as smoothing filters, regression computations, covariance estimatio...

A new formalism in the finite difference framework is developed, which consists of three steps: choosing the dimension of the local approximation subspace, constructing a vector basis for this subspace, and determining the coefficients of the linear combination [1, 3]. This new approach called the Complete Method is capable to generate any finite d...

Achieving high-order accuracy in finite difference/spectral methods for space-time fractional differential equations often relies on very restrictive and usually unrealistic smoothness assumptions in the spatial and/or temporal domains. For spatial discretization, spectral methods using smooth basis functions are commonly employed. However, spatial...

The volume-of-fluid (VOF) method is widely used for multiphase flow simulations, where the VOF function implicitly represents the interface through the volume fraction field. The height function (HF) method on a Cartesian grid integrates the volume fractions of a column of cells across the interface. A stencil of three consecutive heights and cente...

Resistance factors for pile groups are typically derived using empirical methods that do not directly account for system redundancy and overlook the correlation between individual piles, which are inherently influenced by the spatial variability of soils. While rigorous three-dimensional (3D) random finite difference (RFD) or random finite element...

Tuberculosis (TB) and human immunodeficiency virus (HIV)/acquired immunodeficiency virus (AIDS) have a fatal bidirectional connection with a significant global epidemic overlap. People living with HIV-positive are over 30 times more likely than HIV-negative people to develop TB and active TB causes the chronic immunological activation, which accele...

Predicting the development of cracking processes in structural elements made of reinforced concrete (RC) or other cementitious composites is still a challenging task. Although well‐established experimental procedures are widely adopted with the aim to gain empirical knowledge of the aforementioned processes, no similar consensus has been reached ab...

This paper presents the development of the hybrid method of mimetic finite difference (MFD) and discontinuous Galerkin (DG) for polymer flooding and an in-depth study of its computational performance. The proposed hybrid method, simply denoted by MFD-DG method, initially discretizes pressure equations using the MFD method to calculate the pressure...

This paper introduces a novel framework, the unified closest point method (CPM) using the least-squares generalized finite difference method (LS-GFDM), to solve the surface partial differential equations (PDEs). Our approach addresses key limitations of existing embedding methods by unifying the computation of finite difference weights and interpol...

The prime objective of the investigation is to study the effect of SWCNT nanoparticles in the base fluid Ethylene glycol on the hydrodynamics and heat transmission through a stretching surface in a Darcy–Forchheimer porous regime. The novelty of the investigation is to examine the behaviour of the heat conduction due to superior thermal conductivit...

The study of bioconvective flow of Casson-Williamson nanoliquid over a rough slender cylinder has many engineering and industrial applications. However, limited research exists on such type of flow under the combined effects of inclined magnetic field and liquid oxygen diffusion in conjunction with nanoparticles. The current research fill this gap...

Understanding how the refractive index of water changes with wavelength under different physical and chemical conditions, such as temperature or pressure, is crucial for describing the behavior of light as it travels through, reflects from, and is absorbed by water. The refractive index can act as an in situ indicator of various physical properties...

The computational complexity of simulating seismic waves demands continual exploration of more efficient numerical methods. While Finite Volume methods are widely acclaimed for tackling general nonlinear hyperbolic (wave) problems, their application in realistic seismic wave simulation remains uncommon, with rare investigations in the literature. F...

Here, we reported the excitation of multiple localized surface plasmons in disk supershape shell nanoparticles using the finite difference time domain method. All plasmon bands of disk supershape shell nanoparticles were extracted from extinction spectra. The characteristics of the plasmon bands were investigated as functions of the structural para...

We investigate the interior Sobolev regularity of weak solutions to the nonlocal $(1, p)$-Laplace equations in the superquadratic case $p\ge 2$. More precisely, for the fractional differentiability index $s_p\in \left(0, \frac{p-1}{p}\right]$, we establish that the weak solution $u$ exhibits $W_{\rm loc}^{\gamma, q}$-regularity for any $\gamma\in \l...

This study considers the pre- and post-breaking behavior of Weakly-nonlinear (WNL) and Fully-nonlinear (FNL) Boussinesq-type (BTE) models. The main inquiries are: 1. Can the FNL model accurately reproduce shoaling behavior and the estimation of parameters crucial for describing breaking initiation? 2. How can the depiction of breaking be enhanced t...

A highly efficient metamaterial absorber is designed for terahertz (THz) sensing and multiband super absorption, utilizing plasmonic and metamaterial properties to achieve nearly perfect absorption across multiple frequencies. The proposed microstructure design (53 μm × 55 μm) is composed on a full ground layer and a multiple concentric squared pat...

This study simulates the thermal behaviour of floating photovoltaic modules under varying conditions of plane-of-array irradiance, wind speed, air temperature, and water temperature. A transient, one-dimensional finite difference model calculates cell temperature, efficiency, and power output. Validated using 46 days of experimental data from a flo...

Continual Learning (CL) aims to enable models to continuously acquire new knowledge from a sequence of tasks with avoiding the forgetting of learned information. However, existing CL methods only rely on the parameters of the most recent task for inference, which makes them susceptible to catastrophic forgetting. Inspired by the recent success of m...

In this work, we present a training method for a Fully Quantum Neural Network (FQNN) based entirely on quantum circuits. The model processes data exclusively through quantum operations, without incorporating classical neural network layers. In the proposed architecture, the roles of classical neurons and weights are assumed, respectively, by qubits...

This continuation presents analytical and numerical simulations for unsteady laminar flow of Maxwell nanofluid subject to decomposition of microbes driven by a porous stretching surface. The fluctuation in mass and heat transmission is proceeded with variable assumptions of thermal conductivity and mass diffusivity. Moreover, the heat source and ac...

In this report, a new strategy for solving systems of nonlinear algebraic equations is presented. The proposed method is a quasi-Newton approximation corresponding to a multidimensional extension of the well-known secant method. Unlike other quasi-Newton methods (e.g., Broyden's method) that continually update the Jacobian (or its inverse) after ea...

Shadows are common in many types of images, causing information loss or disturbance. Shadow removal can help improve the quality of the digital image. If there is no effective information available to restore the original image in the shaded area, the interpolation‐based inpainting technique can be used to remove the shadow from the digital image....

The use of boundary integral equations in modeling boundary value problems-such as elastic, acoustic, or electromagnetic ones-is well established in the literature and widespread in practical applications. These equations are typically solved numerically using boundary element methods (BEMs), which generally provide accurate and reliable solutions....

We live in an era of significant societal values and priorities shifts. For centuries, economic growth was the central aim of human development, while sustainability was missed. To achieve carbon neutrality (CN), circularity of material is crucial. One solution is to recycle demolished concrete as aggregate and recycled steel fibers that improve th...

The research aims to investigate the impacts of isothermal heat and species (mass) flux models on the phenomena of thermal as well as species (mass) transference aspects of nanofluid composed of water that is (Al2O3, Cu, Ag and TiO2 in Table 1) located over a upright cone in the process of viscidity dissipation, MHD, chemical process, thermic radia...

Calculation of high-order vertical derivatives represents a fundamental challenge in gravity and magnetic data processing, with critical applications in potential field separation, continuation analysis, and geological boundary identification. Conventional methods for obtaining these derivatives often face stability limitations, particularly when c...

This research focuses on pneumococcal pneumonia respiratory infection caused by Streptococcus pneumoniae bacteria by considering various epidemiological aspects. Researchers have discovered that elevating vaccination and hospitalization rates results in a decline in pneumococcal pneumonia disease cases. This study examines an epidemic model incorpo...

Zamanın yönü (arrow of time) fiziksel olayların zamanda hangi yönde (ileri veya geri) meydana geldiğini gösterir. Prensip olarak frekans uzayındaki çözümler zaman parametresini içermediğinden zamanın yönünü açıklayamaz. Bu nedenle öncelikle zaman uzayına geçilerek çözüm yapılmalıdır. Klasik olarak ters Fourier dönüşümü ile elde edilen zaman uzayı ç...

The study of heat transfer across various skin tissue geometries is crucial in the treatment of tumors. A novel mathematical bioheat transfer model is developed by introducing the shape parameter of skin tissues: cylindrical, spherical, and slab. The whole model is transformed into a dimensionless form. The problem is discretized into a generalized...

This review paper will highlight the versatility of meshless radial basis functions that are used to solve numerically linear and nonlinear integral equations (IEs), elliptic, hyperbolic, and parabolic partial differential equations (PDEs), and integto partial differential equations (IPDEs). In addition, this review will show that the classic well-...

The lid-driven cavity flow serves as a fundamental benchmark in computational fluid dynamics (CFD), valued for its simple geometry and complex flow patterns, making it an ideal testbed for validating numerical methods. Traditional numerical approaches, such as finite difference and finite element methods, often require substantial computational res...

The impacts of variable thermal conductivity and entropy generation in the MHD flow of Williamson nanofluid between stretching axisymmetric discs, considering nonlinear thermal radiation and non-uniform heat generation parameters, have been numerically simulated in this article. The proposed model’s partial differential equations are converted into...

We introduce a novel class of finite difference approximations, termed zigzag schemes, that employ a hybrid stencil that is neither symmetrical, nor fully one-sided. These zigzag schemes often enjoy more permissive stability constraints and see their coefficients vanish as the order tends to infinity. This property permits the formulation of higher...

This paper aimed at proving first order convergence for system of two singularly perturbed time-dependent initial value problems with delay in spatial variable and robin initial conditions. A Classical layer resolving finite difference scheme is developed by implementing uniform mesh for time discretization; Shishkin-mesh, a piecewise uniform mesh...

Classic active contour models (ACMs) are becoming a great promising solution to the contour-based object extraction with the progress of deep learning recently. Inspired by the wave vibration theory in physics, we propose a Generalized Contour Vibration Model (G-CVM) by inheriting the force and motion principle of contour wave for automatically est...

Simulating hypersonic flow presents many computational challenges and requires use of software that can handle a wide range of external conditions. In general, hypersonic flight occurs at high altitude with flow regimes from the continuum, where the conventional no-slip boundary condition is appropriate, through to the free molecular regime, where...

We propose a method for measuring instantaneous structural intensity (SI) in flat structures using finite difference approximations. Based on flat plate theory, stress components associated with axial forces, bending moments, torsional moments, and shear forces are described in terms of vibration displacement. The derivation formulation is establis...

This numerical research presents a sustainable system for freshwater extraction from wastewater, utilizing a solar thermal-driven membrane process powered by solar energy. The efficiency of the newly proposed system is evaluated by developing a thermal model and solving it through a finite difference approach. Individually validated the condenser a...

A highly sensitive sensor based on metal–insulator-metal nanostructure with new branches is proposed. The performance of this sensor is based on measuring the refractive index of the sensing materials. This measurement is used to diagnose medical conditions such as cancer, diabetes, and blood infections by detecting small changes in the refractive...

In two well-known studies [Mathematics and Computers in Simulation 79(2008) 622-633] and [Mathematics and Computers in Simulation 182(2021) 397-410], some nonstandard finite difference (NSFD) schemes for an SIRC epidemic model of influenza A have been proposed. There have been attempts to prove that these NSFD schemes can preserve the positivity of...

This paper is concerned with the boundary layer on the leading edge of an aerofoil with the aerofoil surface sliding parallel to itself in the upstream direction. The flow analysis is conducted in the framework of the classical Prandtl formulation with the pressure distribution given by the solution for the outer inviscid flow. Since a reverse flow...

This study investigates unsteady, reactive magnetohydrodynamic (MHD) Eyring-Powell fluid in a microchannel, incorporating suction/injection and heat source effects. The governing nonlinear deterministic two-variables differential equations, derived from the principles of conservation of mass, momentum, and species concentration, are transformed int...

To study the channel characteristics and communication performance in the low‐frequency UWB band for head‐mounted devices, this paper uses the finite difference time domain method, combined with the electromagnetic properties of human tissues, to establish a human head model. It proposes a head transmission system under the low‐frequency UWB band,...

In the pursuit of enhanced oil recovery (EOR), polymer flooding plays a crucial role. However, traditional grid-based methods for simulating polymer flooding seepage face challenges such as complex grid generation and potential grid-related issues. This paper presents a numerical seepage model for polymer-flooding reservoirs based on the generalize...

This paper focuses on RBF-based meshless methods for approximating differential operators, one of the most popular being RBF-FD. Recently, a hybrid approach was introduced that combines RBF interpolation and traditional finite difference stencils. We compare the accuracy of this method and RBF-FD on a two-dimensional Poisson problem for standard fi...

Thermal behaviour in directed energy deposition (DED) governs both the microstructural evolution of deposited layers and the distribution of residual stresses. However, the effect of airflow field at the nozzle on the thermal history is unclear at present. Here, a temperature field predicted model was developed to investigate the thermal changes in...

My research focuses on the theoretical and numerical study of Hamilton-Jacobi-Bellman (HJB) equations, which are central to optimal control theory. The work combines finite element and finite difference methods, with the use of quasi-variational inequalities (QVIs) and monotone iterative algorithms, providing rigorous convergence analysis and pract...

This paper presents the application of the Modified TOR (MTOR) method, implemented using CUDA, for solving Poisson's equation through the iterative Finite Difference (FD) method. The study aims to provide a detailed description of the MTOR method for solving Partial Differential Equations (PDEs) on both standard and rotated meshes, employing CUDA f...

When employing bonded discrete element models (DEMs) to model rocks, a fundamental problem is how to determine the micro parameters to accurately simulate the rock strength characteristics. One promising way to improve calibration efficiency is to fully utilize the underlying relationship between DEM micro parameters and the macro strengths of rock...

In the paper developed and numerically solved the problem of solute transport in a porous medium consisting of active and passive zones, taking into account the multi-stage nature of adsorption kinetics. A mathematical model of the process is compiled based on general conservation laws and additional phenomenological assumptions. The influence of i...

The work presents a study of the non-linear mathematical model of tumor growth, proposed by Kolev and Zubik-Kowal (2011). The model is described by a system composed of four partial differential equations that represent the evolution of the density of cancer cells, density of the extracellular matrix (ECM), concentration of matrix-degrading enzyme...

In this manuscript, we introduce an SEIVR model for COVID-19 and conduct a stability and numerical analysis. The stability of the integral-order system is examined using the Routh-Hurwitz criterion for local stability and the Lyapunov function for global stability. The basic reproduction number \documentclass[12pt]{minimal} \usepackage{amsmath} \us...

This work investigates the concept of numerically approximating fractional differential equations (FDEs) by using function average in an interval. First, the equivalent integral equation is obtained. Then, averaging methods (first-order product integration methods), such as Euler and midpoint, consist in replacing the right-hand side of the FDE by...

We establish the notion of limit consistency as a modular part in proving the consistency of lattice Boltzmann equations (LBEs) with respect to a given partial differential equation (PDE) system. The incompressible Navier--Stokes equations (NSE) are used as a paragon. Based upon the hydrodynamic limit of the Bhatnagar-Gross-Krook (BGK) Boltzmann eq...

In this paper, we consider a modified Benjamin–Bona–Mahony (BBM) equation, which, for example, arises in shallow-water models. We discuss the well-posedness of the Dirichlet initial-boundary-value problem for the BBM equation. Our focus is on identifying a time-dependent source based on integral observation. First, we reformulate this inverse probl...

This manuscript proposes an efficient hybrid numerical approach that combines high accuracy with low computational cost to approximate solutions of the time-space diffusion model governed by the Caputo and Riesz fractional derivatives. Addressing the fractional time derivative in the Caputo sense, we employ a combination of quadratic and linear int...

This study proposes a high-temperature arc discharge pretreatment method to enhance the photosensitivity of hydrogen-loaded germanium-doped fibers for single-pulse FBG inscription. By coupling hydrogen diffusion dynamics with hydroxyl reaction kinetics, a numerical model based on Fick's law and Arrhenius equations was established. Finite difference...

Despite the fact that experimental and theoretical work on the spectrum of methoxy has stretched from the microwave to the ultraviolet and proceeded for nearly 50 years, parts of the spectrum have remained a challenge to simulate theoretically and make reliable line-by-line assignments. The spectral complexity arises because the radical has a non-z...

Accurate and efficient modeling of the Laser Interferometer Space Antenna (LISA) response is crucial for gravitational-wave (GW) data analysis. A key computational challenge lies in evaluating time-delay interferometry (TDI) variables, which require projecting GW polarizations onto the LISA arms at different retarded times. Without approximations,...

This work investigates the dispersion of uncharged solutes driven by fluid convection, considering two distinct flow mechanisms: pressure-driven flow (PDF) and electroosmotic flow (EOF). In PDF, the convective flow arises from an applied pressure gradient. On the other hand, the EOF is generated by an applied electric field interacting with the net...

In this study, a statistical estimation is done for an epidemic model of cryptosporidiosis by changing it into a fractional order system. The disease-free equilibrium point, and the endemic equilibrium point are the two equilibrium points and Jacobian matrix theory is used to determine stability. The basic reproductive number R0 is calculated and e...