Bongsoo Jang

Ulsan National Institute of Science and Technology | UNIST · Mathematical Sciences

Thermal energy storage systems, heat exchangers, and electronic devices often encounter significant challenges, such as inadequate heat transport and excessive overheating. To mitigate these issues, enhancing convective heat transfer through the use of nanofluids offers a promising solution. Additionally, incorporating fins to augment surface area...

This study comprehensively explores a unified methodology for deriving exact solutions to the fractional modified (3+1) dimensional Kudryashov–Sinelshchikov (KS) equation featuring variable coefficients. The fractional KS equation, which incorporates fractional local M-derivatives, presents a significant challenge because of its inherent nonlineari...

Solar collectors are devices that transform solar irradiation energy into thermal energy for various purposes. Among different solar thermal collectors, solar dish collectors are remarkable for having the highest solar-to-thermal energy conversion efficiency. These collectors are available with various receiver shapes like external, cavity, spiral...

In this article, a considerably efficient predictor-corrector method (PCM) for solving Atangana–Baleanu Caputo (ABC) fractional differential equations (FDEs) is introduced. First, we propose a conventional PCM whose computational speed scales with quadratic time complexity O(N2) as the number of time steps N grows. A fast algorithm to reduce the co...

Fins, referred to as extended surfaces, play a crucial role in enhancing heat transfer across various industrial sectors. They achieve this by increasing the surface area available for convective heat transfer. These widespread applications span fields such as energy production, mechanical engineering, surface studies, heat recovery processes, and...

This study comprehensively explores a unified methodology for deriving exact solutions to the fractional modified (3+1) dimensional Kudryashov-Sinelshchikov (KS) equation featuring variable coefficients. The fractional KS equation, which incorporates fractional local M-derivatives, presents a significant challenge because of its inherent nonlineari...

Purpose The need for precise synthesis of customized designs has resulted in the development of advanced coating processes for modern nanomaterials. Achieving accuracy in these processes requires a deep understanding of thermophysical behavior, rheology and complex chemical reactions. The manufacturing flow processes for these coatings are intricat...

Reservoir computing, one of the state-of-the-art machine learning architectures, processes time-series data generated by dynamical systems. Nevertheless, we have realized that reservoir computing with the conventional single-reservoir structure suffers from capacity saturation. This leads to performance stagnation in practice. Therefore, we propose...

The current article deals with the computational study of buoyant convection and heat dissipation processes of hybrid nanoliquid saturated in an inclined porous annulus. The fluid flow movement in the porous annular region is modeled using Darcy-Brinkman-Forchheimer model. The vertical boundaries of the cylinder are subjected to uniform but differe...

In this paper, we present a new fractional epidemiological model on a heterogeneous network to investigate Middle East respiratory syndrome (MERS-CoV), which is caused by a virus in the coronavirus family. We also consider the development of equations for the camel population, given that it is the primary animal source of the virus, as well as dire...

The present investigation is devoted to analyze the buoyancy-driven flow behavior and associated thermal dissipation rate in a nanofluid-filled annular region with five different single source-sink and three different dual source-sink arrangements along the vertical surfaces. The remaining region on the vertical boundaries and horizontal surfaces a...

While network-based techniques have shown outstanding performance in image denoising in the big data regime requiring massive datasets and expensive computation, mathematical understanding of their working principles is very limited. Not to mention, their relevance to traditional mathematical approaches has not attracted much attention. Therefore,...

This article proposes new strategies for solving two-point Fractional order Nonlinear Boundary Value Problems (FNBVPs) with Robin Boundary Conditions (RBCs). In the new numerical schemes, a two-point FNBVP is transformed into a system of Fractional order Initial Value Problems (FIVPs) with unknown Initial Conditions (ICs). To approximate ICs in the...

Efficient and fast explicit methods are proposed to solve nonlinear Caputo-Fabrizio fractional differential equations, where Caputo-Fabrizio operator is a new proposed fractional derivative with a smooth kernel. The proposed methods produce the second-order for linear interpolation and the third-order accuracy for quadratic interpolation, respectiv...

One of the common assumptions in previous spatial dynamics of cyclic competition is that, regardless of competing structure and strength among species, the spatial size of a network is considered as large as possible to avoid finite size effect for species biodiversity. In real ecosystems, however, species richness, which can be defined by spatial...

Efficient and fast predictor-corrector methods are proposed to deal with nonlinear Caputo-Fabrizio fractional differential equations, where Caputo-Fabrizio operator is a new proposed fractional derivative with a smooth kernel. The proposed methods achieve a uniform accuracy order with the second-order scheme for linear interpolation and the third-o...

This article proposes new strategies for solving two-point Fractional order Nonlinear Boundary Value Problems(FN-BVPs) with Robin Boundary Conditions(RBCs). In the new numerical schemes, a two-point FNBVP is transformed into a system of Fractional order Initial Value Problems(FIVPs) with unknown Initial Conditions(ICs). To approximate ICs in the sy...

In this paper, the shifted Jacobi spectral-Galerkin method is introduced to deal with fractional order initial value problems (FIVPs). In the proposed method, the exact solution of the FIVP is approximated by using shifted Jacobi polynomials on each subinterval of the total time. The main advantage of the proposed method is that the rate of converg...

This paper proposes new direct and acceleration numerical methods for solving Fractional order Differential Equations (FDEs). For the Caputo differential operator with fractional order 0 < ν < 1, we rewrite the FDE as an equivalent integral form circumventing the derivative of the solution by the integral by parts. We obtain a discrete formulation...

Alternative strategy is common in animal populations to promote reproductive fitness by obtaining resources. In spatial dynamics of cyclic competition, reproduction can occur when individuals obtain vacant rooms and, in this regard, empty sites should be resources for reproduction which can be induced by interspecific competition. In this paper, we...

A fractional-order predator–prey biological economic system with Holling type II functional response is proposed. Local stability and Hopf bifurcation of predator–prey systems have been investigated in both commensurate and incommensurate fractional-order systems. We explore how the economic profit and fractional orders influence the local stabilit...

Cyclically competition models have been successful to gain an insight of biodiversity mechanism in ecosystems. There are, however, still limitations to elucidate complex phenomena arising in real competition. In this paper, we report that a multistability occurs in a simple rock-paper-scissor cyclically competition model by assuming that intraspeci...

This paper reports the numerical investigation of natural convection in an inclined parallelogrammic porous enclosure. The vertical sloping sidewalls of the enclosure are maintained at different, uniform temperatures, while the top and the bottom walls are kept at adiabatic. Using Darcy’s law, the governing equations are modeled and are solved usin...

Evolutionary games of cyclic competitions have been extensively studied to gain insights into one of the most fundamental phenomena in nature: biodiversity that seems to be excluded by the principle of natural selection. The Rock-Paper-Scissors (RPS) game of three species and its extensions [e.g., the Rock-Paper-Scissors-Lizard-Spock (RPSLS) game]...

An accurate and efficient new class of predictor-corrector schemes are proposed for solving nonlinear differential equations of fractional order. By introducing a new prediction method which is explicit and of the same accuracy order as that of the correction stage, the new schemes achieve a uniform accuracy order regardless of the values of fracti...

Smart devices interconnected through Internet became one of everyday items. In particular, we are now able to access Internet anywhere and anytime with our smartphones. To support the ad-hoc access to Internet by using smartphones, the computer network structure has become more complex. Also, a certain network node is highly connected to support th...

The design basis functions on the reference domain in IGA are diversified and enhanced by extra enrichment functions and various local refinements with the use of partition of unity (PU) function with flat-top. These reconditioned and modified basis functions are pushed forward to the physical domain by the original design mapping for analysis. Wit...

Partition of Unity Isogeometric Analysis of Boundary Layer Problems

This article reports convection heat transfer in short and tall annular enclosure with two discrete isoflux heat sources of different lengths. The discrete heat sources are mounted at the inner wall and the outer wall is maintained at a lower temperature, while the top and bottom walls and the unheated portions of the inner wall are kept at adiabat...

In this work, we present an efficient semi-analytical method based on the Taylor series for solving nonlinear Volterra integro-differential equations, namely the differential transform method (DTM). The DTM provides a recursive relation for the coefficients of the Taylor series that is derived from the given equations. We provide a new recursive re...

In this paper, we propose a new approach of the generalized differential transform method (GDTM) for solving nonlinear fractional differential equations. In GDTM, it is a key to derive a recurrence relation of generalized differential transform (GDT) associated with the solution in the given fractional equation. However, the recurrence relations of...

A numerical investigation of natural convection heat transfer induced by two discrete heat sources placed on the inner wall of a vertical porous annulus has been carried out in this article. The outer wall is maintained at a lower temperature, while top and bottom walls and unheated portions of inner wall are kept adiabatic. The porous medium is mo...

In this paper, we propose a new modification of the multistage generalized differential transform method (MsGDTM) for solving fractional differential equations. In MsGDTM, it is the key how to impose an initial condition in each sub-domain to obtain an accurate approximate solution. In several literature works (Odibat et al. in Comput. Math. Appl....

In this paper, we present the multistage homotopy perturbation method for finding the solution of the chemical kinetics with nonlinear reactions. We develop a general scheme for finding the analytic solution of chemical reaction networks and apply it to motivating chemical examples such as the enzyme kinetics model and the Brusselator model. We ill...

Reproducing Polynomial Particle Method (RPPM) is one of meshless methods that use meshes minimally or do not use meshes at all. In this paper, the RPPM is employed for free vibration analysis of shear-deformable plates of the first order shear deformation model (FSDT), called Reissner-Mindlin plate. For numerical implementation, we use flat-top par...

The present numerical investigation deals with the size and location effects of a single isoflux discrete heater on the buoyancy induced convection in a cylindrical annulus. A discrete heater is placed at the inner wall, while the top and bottom walls as well as the unheated portions of the inner wall are kept adiabatic, and the outer wall is maint...

The differential transform method (DTM) is based on the Taylor series for all variables, but it differs from the traditional Taylor series in calculating coefficients. Even if the DTM is an effective numerical method for solving many nonlinear partial differential equations, there are also some difficulties due to the complex nonlinearity. To overc...

We present an efficient computational algorithm, namely, the enhanced multistage differential transform method (E-MsDTM) for solving prey-predator systems. Since the differential transform method (DTM) is based on the Taylor series, it is difficult to obtain accurate approximate solutions in large domain. To overcome this difficulty, the multistage...

In this work, we propose a novel computational algorithm for solving linear and nonlinear initial value problems by using the modified version of differential transform method (DTM), which is called the projected differential transform method (PDTM). The PDTM can be easily applied to the initial value problems with less computational work. For the...

Tari et al. [A. Tari, M.Y. Rahimi, S. Shahmorad, F. Talati, Solving a class of two-dimensional linear and nonlinear Volterra integral equations by the differential transform method, J. Comput. Appl. Math. 228 (2009) 70-76], presented some fundamental properties of TDTM for the kernel functions in two-dimensional Volterra integral equations. Here, w...

Tari et al. [A. Tari, M.Y. Rahimi, S. Shahmorad, F. Talati, Solving a class of two-dimensional linear and nonlinear Volterra integral equations by the differential transform method, J. Comput. Appl. Math. 228 (2009) 70-76], presented some fundamental properties of TDTM for the kernel functions in two-dimensional Volterra integral equations. Here, w...

New solutions of the auxiliary equation are presented. By using those solutions, many exact travelling wave solutions for the several nonlinear Klein–Gordon equations are explicitly obtained.

The Auxiliary equation method is used to find analytic solutions for the Kawahara and modified Kawahara equations. It is well known that different types of exact solutions of the given auxiliary equation produce new types of exact travelling wave solutions to nonlinear equations. In this paper, new exact solutions of the auxiliary equation are pres...

In this paper, we present an efficient numerical algorithm for solving two-point linear and nonlinear boundary value problems, which is based on the Adomian decomposition method (ADM), namely, the extended ADM (EADM). The proposed method is examined by comparing the results with other methods. Numerical results show that the proposed method is much...

In this paper, we extend the homogeneous Adomain decomposition method (HADM) introduced by Jang [Bongsoo Jang, Exact solutions to one-dimensional non-homogeneous parabolic problems by the homogeneous decomposition method, Appl. Math. Comput. 186 (2) (2007) 969–979] to solve non-homogeneous parabolic partial differential equations with variable coef...

In this paper, we propose a reliable modification of Adomian decomposition method, namely the homogeneous Adomian decomposition method (HADM), that solves one dimensional non-homogeneous parabolic equations with a variable coefficient. The effectiveness of this method is verified through illustrative examples.

The finite element (FE) solutions of a general elliptic equation −div([aij] ⋅∇u) + u = f in an exterior domain Ω, which is the complement of a bounded subset of R3, is considered. The most common approach to deal with exterior domain problems is truncating an unbounded subdomain Ω∞, so that the remaining part ΩB = Ω\Ω∞ is bounded, and imposing an a...

Recently Babus̆ka-Oh introduced the method of auxiliary mapping (MAM) which efficiently handles elliptic boundary value problems containing singularities. In this paper, a special weighted residue method, the Weighted Ritz-Galerkin Method (WRGM), is investigated by introducing special weight functions. Together with this method, MAM is modified to...

this paper, the Weighted Riesz-Galerkin Method (WRGM) is investigated by introducing special weight functions. Together with this method, MAM is modified to yield highly accurate finite element solutions to general elliptic boundary value problems on the exterior of bounded domains at low cost. 1.

Extinction of species has been one of the biggest mysteries in nature. A dynamical model for the species extinction is very complex because each species interacts with many other species as well as physical factors such as weather. Therefore it looks difficult to determine the structure of food chain mathematically. However, in certain situations t...

In order to reduce the computational work in multi-scale media, the homogenization theory has been applied in many fields. The key step for the homogenization is to calculate effective coeffi- cients. In this work, we demonstrate how to approximate an unknown effective coefficient from the known effective coefficients. In other words, suppose that...

In recent work, author in [1] employed the modified differential transform method(MDTM) for solving fractional Chen system. He derived numerical solutions by the MDTM with frac-tional order α = 0.99 and compared the results with ones obtained by the generalized Adams-Bashforth-Moulton method(GABMM), which is well know method for solving fractional...

In recent years the dynamics of fractional order system have been interested in many fields. We studied numerically the bifurcations and chaotic investigation in the several fractional-order systems, especially simplified Lorenz system. We have investigated the complex dynamics by presenting phase portraits, bifurcation diagram and Lyapunov exponen...

Thesis (Ph. D.)--University of Oklahoma, 1988. Includes bibliographical references (leaves 61-63).