# Dr Ram JiwariIndian Institute of Technology Roorkee | University of Roorkee · Department of Mathematics

Dr Ram Jiwari

Ph.D (Numerical Analysis)

## About

81

Publications

32,447

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1,966

Citations

Citations since 2017

Introduction

Additional affiliations

May 2014 - August 2016

May 2011 - September 2013

## Publications

Publications (81)

The hyperbolic nonlinear Schrödinger equation in the (3 + 1)-dimension depicts the evolution of the elevation of the water wave surface for slowly modulated wave trains in deep water. Many researchers have studied the applicability and practicality of this model, but the analytical approach has been virtually absent from the literature. We adapted...

The current study is dedicated to find the complex soliton solutions of the hyperbolic (2+1)-dimensional nonlinear Schrödinger equation. In this direction we takes the help of Lie Symmetry analysis method. First of all we obtained the invariant condition which play important role in the mechanism of Lie symmetry method. After that we obtained the s...

In this paper, we first examine the type of structure of the solutions to the modified form of a nonlinear Fisher’s reaction-diffusion equation. The existence of the traveling wave solution to the equation in the long term is observed by using dynamical system theory and exhibiting a phase space analysis of its stable points. In parallel, we repres...

The current study dedicated to the compressible isentropic Navier–Stokes equations in one-dimensional with a general
pressure law. The Lie Group method is employed to reduce the compressible Navier–Stokes equations to a system of highly
nonlinear ordinary differential equations with suitable similarity transformations. Consequently, with the help o...

Diffusion plays a significant role in complex pattern formulations occurred in biological and chemical reactions. In this work, the authors study the effect of diffusion in coupled reaction-diffusion systems named the Gray-Scott model for complex pattern formation with the help of cubic B-spline quasi-interpolation (CBSQI) method and capture variou...

This work analyses the features of nanofluid flow and thermal transmission (NFTT) in a rectangular channel which is asymmetric by developing two numerical algorithms based on scale-2 Haar wavelets (S2HWs), Lagrange’s interpolation differential quadrature technique (LIDQT), and quasilinearization process (QP). In the simulation procedure, first of a...

This work analyze singularly perturbed convection-diffusion-reaction (CDR) models with two parameters and variable coefficients by developing a mesh-free scheme based on local radial basis function-finite difference (LRBF-FD) approximation. In the evolvement of the scheme, time derivative is discretized by forward finite difference. After that, LRB...

In this article, with the help of Legendre wavelets a hybrid approach is presented for the numerical solution of the Helmholtz equation which has a complex solution. The present hybrid approach is based on the Legendre Wavelet Collocation Method (LWCM). Initially, the Helmholtz equation is converted to the coupled equation with suitable transformat...

This work analyze singularly perturbed Burgers’ model by developing two meshfree algorithms based on local radial basis function-finite difference approximation. The main goal of this task is to present computational modeling of the model when perturbation parameter ɛ→0 where most of the traditional numerical methods fail. In the evolvement of the...

This work offers two radial basis functions (RBFs) based meshfree schemes for the numerical simulation of non-linear extended Fisher-Kolmogorov model. In the development of the first scheme, first of all, time derivative is discretized by forward finite difference and then stability and convergence of the semi-discrete model is analyzed in L2 and H...

Recently, many authors studied the numerical solution of the classical Darboux problem in it's integral form via two-dimensional nonlinear Volterra-Fredholm integral equation. In the present article, a numerical technique based on the Cheby-shev wavelet is proposed to solve the Darboux problem directly without converting into a nonlinear Volterra F...

In this article, the authors simulate and study dark and bright soliton solutions of 1D and 2D regularized long wave (RLW) models. The RLW model occurred in various fields such as shallow-water waves, plasma drift waves, longitudinal dispersive waves in elastic rods, rotating flow down a tube, and the anharmonic lattice and pressure waves in liquid...

Purpose
This paper aims to develop a meshfree algorithm based on local radial basis functions (RBFs) combined with the differential quadrature (DQ) method to provide numerical approximations of the solutions of time-dependent, nonlinear and spatially one-dimensional reaction-diffusion systems and to capture their evolving patterns. The combination...

In this article, barycentric rational interpolation and local radial basis functions (RBFs) based numerical algorithms are developed for solving multidimensional sine‐Gordon (SG) equation. In the development of these algorithms, the first step is to drive a semi‐discretization in time with a finite difference, and then the semi‐discrete problem is...

In this work, we present two approaches for simulation of fourth-order parabolic partial differential equations. In the first method, cubic B-spline quasi-interpolation is used to approximate the spatial derivative of the dependent variable and forward difference to approximate the time derivative. In the second method, we have used modified cubic...

In this work, a numerical algorithm is developed with the help of Legendre wavelets and quasilinearization method for simulation of Multidimensional Benjamin-Bona-Mahony-Burgers (BBMB) and Sobolev equations. Initially, non-linear equation is linearized by quasilinearization method and then Legendre wavelets are used for both space and temporal disc...

In this article, the authors proposed a meshfree approach for simulation of non-linear Schrödinger equation with constant and variable coefficients. Schrödinger equation is a classical field equation whose principal applications are to the propagation of light in non-linear optical fibers and planar waveguides and in quantum mechanics. First of all...

In this paper, a quasilinearization based Legendre wavelet numerical scheme is proposed for time-dependent one dimensional Burgers' and coupled Burgers' equation. The present method is completely independent of time discretization contrast to the recent literature for time discretization based on wavelet scheme for Burgers' and coupled Burgers' equ...

Purpose
The purpose of this study is to extend the cubic B-spline quasi-interpolation (CBSQI) method via Kronecker product for solving 2D unsteady advection-diffusion equation. The CBSQI method has been used for solving 1D problems in literature so far. This study seeks to use the idea of a Kronecker product to extend the method for 2D problems.
D...

In this paper a quasilinearization based Legendre wavelet numerical scheme is proposed for time dependent one dimensional Burgers’ and coupled Burgers’ equation. The present method is completely independent of time disctrization contrast to the recent literature for time disctrization based on wavelet scheme for Burgers’ and coupled Burgers’ equati...

This work proposes a numerical scheme based on Legendre wavelets and quasilinearization for 1D, 2D, and 3D Benjamin-Bona-Mahony-Burgers (BBM) equation. Firstly, nonlinear equation is linearized by quasilinearization and later a numerical scheme is developed based on Legendre wavelets without the help of finite-difference scheme. In this approach, a...

In this work, a numerical algorithm is developed with the help of Legendre wavelets for simulation of time-dependent three-dimensional (3D) Benjamin{Bona-Mahony-Burgers (BBMB) and Sobolev equations. Initially, non-linear equation is linearized by quasilinearization method and then Legendre wavelets are used for space and temporal discretization. Th...

In this work, the authors developed two new B-spline
collocation algorithms based on cubic trigonometric B-spline functions to find approximate solutions of nonlinear parabolic partial differential equations (PDEs) with Dirichlet and Neumann boundary conditions. In the first algorithm, cubic trigonometric B-spline functions are directly used for ap...

The purpose of this paper is to develop two meshfree algorithms based on multiquadric radial basis functions (RBFs) and differential quadrature (DQ) technique for numerical simulation and to capture the shocks behavior of Burgers’ type problems.
Two meshfree algorithms are developed and their stability is discussed. Numerical experiment is done to...

In this article, the authors approximate solution to the Brusselator model by Galerkin finite element method and present a priori error estimate for the approximation. Further, we study the stability of the model when cross-diffusion is present. We find that the cross-diffusion increases the wave number of the solution. Using Crank–Nicolson method...

In this article, we study some soliton-type analytical solutions of Schrödinger equation, with their numerical treatment by Galerkin finite element method. First of all, some analytical solutions to the equation are obtained for different values of parameters; thereafter, the problem of truncating infinite domain to finite interval is taken up and...

The main focus of this article is to capture the patterns of reaction–diffusion Brusselator
model arising in chemical processes such as enzymatic reaction, formation of
turing patterns on animal skin, formation of ozone by atomic oxygen through a triple
collision. For this purpose, a meshfree algorithm is developed based on radial basis
multiquadri...

In this article, we establish the existence and uniqueness of solutions to the coupled reaction–diffusion models using Banach fixed point theorem. The Galerkin finite element method is used for the approximation of solutions, and an a priori error estimate is derived for such approximations. A scheme is proposed by combining the Crank–Nicolson and...

Purpose
This paper aims to capture the effective behaviour of nonlinear coupled advection-diffusion-reaction systems and develop a new computational scheme based on differential quadrature method.
Design/methodology/approach
The developed scheme converts the coupled system into a system of ordinary differential equations. Finally, the obtained sys...

This work deals to capture the different types of patterns of nonlinear time dependent coupled reaction-diffusion models. To accomplish this work, a new differential quadrature (DQ) algorithm is developed with the help of modified trigonometric cubic B-spline functions. The stability part of the developed algorithm is studied by matrix stability an...

Purpose
The purpose of this study is to develop an algorithm for approximate solutions of nonlinear hyperbolic partial differential equations.
Design/methodology/approach
In this paper, an algorithm based on the Haar wavelets operational matrix for computational modelling of nonlinear hyperbolic type wave equations has been developed. These types...

Antimirov’s partial derivatives are used in classical
automata theory for the conversion of regular expressions to
finite automata, tree regular expressions to tree automata, and
ω−regular expressions to Büchi automata. In this paper, we
describe a new variant of the Antimirov’s partial derivatives for
the conversion of fuzzy regular expressions to...

Purpose
The main purpose of this work is the development of a numerical algorithm based on modified cubic trigonometric B-spline functions for computational modelling of hyperbolic-type wave equations. These types of equations describe a variety of physical models in the vibrations of structures, nonlinear optics, quantum field theory and solid-sta...

In this article, the authors present finite element analysis and approximation of Burgers’-Fisher equation. Existence and uniqueness of weak solution is proved by Galerkin's finite element method for non-smooth initial data. Next, a priori error estimates of semi-discrete solution in norm, are derived and the convergence of semi-discrete solution i...

In this paper, the authors proposed a method based on exponential modified cubic B-spline differential quadrature method (Expo-MCB-DQM) for the numerical simulation of three dimensional (3D) nonlinear wave equations subject to appropriate initial and boundary conditions. This work extends the idea of [10] for 3D nonlinear wave type problems. Expo-...

2017) "Haar wavelet quasilinearization approach for MHD Falkner–Skan flow over permeable wall via Lie group method" Access to this document was granted through an Emerald subscription provided by emerald-srm:393769 [] For Authors If you would like to write for this, or any other Emerald publication, then please use our Emerald for Authors service i...

2017) "Haar wavelet quasilinearization approach for MHD Falkner–Skan flow over permeable wall via Lie group method" Access to this document was granted through an Emerald subscription provided by emerald-srm:393769 [] For Authors If you would like to write for this, or any other Emerald publication, then please use our Emerald for Authors service i...

In this paper, a numerical scheme for a parameter identification problem is
presented. The problem here considered is the identification of the stiffness
of structural elements and a new procedure to solve it is proposed. This
procedure involves not only the usual Newton{like iterative algorithm for
nonlinear least squares problems, but it also pro...

In this paper, the authors developed a new differential quadrature method "exponential modified cubic B-spline differential quadrature method (Expo-MCB-DQM)” by using exponential modified cubic B-spline functions as test functions in the traditional differential quadrature method [32]. The new method is tested on one and two dimensional nonlinear B...

Purpose
This paper aims to deal with two-dimensional magneto-hydrodynamic (MHD) Falkner–Skan boundary layer flow of an incompressible viscous electrically conducting fluid over a permeable wall in the presence of a magnetic field.
Design/methodology/approach
Using the Lie group approach, the Lie algebra of infinitesimal generators of equivalence t...

Purpose
The main aim of the paper is to develop a new B-splines collocation algorithm based on modified cubic trigonometric B-spline functions to find approximate solutions of nonlinear parabolic Burgers’-type equations with Dirichlet boundary conditions.
Design/methodology/approach
A modification is made in cubic trigonometric B-spline functions...

The concept of transitive closure is useful for the conversion of classical finite automata into regular expressions. In this paper, we generalize and extend the concept of transitive closure for the conversion of fuzzy automata into fuzzy regular expressions. We prove that, for a fuzzy automaton M where r is a fuzzy regular expression obtained usi...

Inspired by the applications of fuzzy automata and parallel regular expressions, we propose a new mathematical concept of
parallel fuzzy regular expressions. In this paper, we investigate the equivalence between parallel fuzzy regular expressions
and parallel fuzzy finite automata. An algorithm is proposed for carrying out the conversion of paralle...

Purpose
– The purpose of this paper is to present the computational modeling of second-order two-dimensional nonlinear hyperbolic equations by using cosine expansion-based differential quadrature method (CDQM).
Design/methodology/approach
– The CDQM reduced the equations into a system of second-order differential equations. The obtained system is...

In this article, the author proposed two differential quadrature methods to find the approximate solution of one and two dimensional hyperbolic partial differential equations with Dirichlet and Neumann’s boundary conditions. The methods are based on Lagrange interpolation and modified cubic B-splines respectively. The proposed methods reduced the h...

In this article, a hybrid numerical scheme based on Euler implicit method, quasilinearization and uniform Haar wavelets has been developed for the numerical solutions of Burgers’ equation. Most of the numerical methods available in the literature fail to capture the physical behavior of the equations when viscosity . In Jiwari (2012), the author pr...

Using the Lie symmetry approach, the authors have examined exact and numerical solutions of coupled short pulse equation with time-dependent coefficients. The method reduces the system of partial differential equations to a system of ordinary differential equations according to the Lie symmetry admitted. In particular, we found the relevant system...

Purpose
– The purpose of this paper is to propose a numerical scheme based on forward finite difference, quasi-linearisation process and polynomial differential quadrature method to find the numerical solutions of nonlinear Klein-Gordon equation with Dirichlet and Neumann boundary condition.
Design/methodology/approach
– In first step, time deriva...

In this article, the authors study analytic and numerical solutions of nonlinear diffusion equations of Fisher’s type with the help of classical Lie symmetry method. Lie symmetries are used to reduce the equations into ordinary differential equations (ODEs). Lie group classification with respect to time dependent coefficient and optimal system of o...

In this paper, polynomial differential quadrature method (PDQM) is applied to find the numerical solution of the generalized Fitzhugh–Nagumo equation with time-dependent coefficients in one dimensional space. The PDQM reduces the problem into a system of first order non-linear differential equations. Then, the obtained system is solved by optimal f...

In this article, the authors proposed a modified cubic B-spline differential quadrature method (MCB-DQM) to show computational modeling of two-dimensional reaction–diffusion Brusselator system with Neumann boundary conditions arising in chemical processes. The system arises in the mathematical modeling of chemical systems such as in enzymatic react...

In this paper, the variable-coefficient diffusion—advection (DA) equation, which arises in modeling various physical phenomena, is studied by the Lie symmetry approach. The similarity reductions are derived by determining the complete sets of point symmetries of this equation, and then exact and numerical solutions are reported for the reduced seco...

Purpose
– The purpose of this paper is to propose a numerical technique based on polynomial differential quadrature method (PDQM) to find the numerical solutions of two-space-dimensional quasilinear hyperbolic partial differential equations subject to appropriate Dirichlet and Neumann boundary conditions.
Design/methodology/approach
– The PDQM red...

In this paper, a variable-coefficient Benjamin—Bona—Mahony—Burger (BBMB) equation arising as a mathematical model of propagation of small-amplitude long waves in nonlinear dispersive media is investigated. The integrability of such an equation is studied with Painlevé analysis. The Lie symmetry method is performed for the BBMB equation and then sim...

The Lie symmetry analysis is performed for the coupled short plus (CSP) equation. We derive the infinitesimals that admit the classical symmetry group. Five types arise depending on the nature of the Lie symmetry generator. In all types, we find reductions in terms of system of ordinary differential equations, and exact solutions of the CSP equatio...

In this work, a numerical scheme based on weighted average differential quadrature method is proposed to solve time dependent Burgers’ equation with appropriate initial and boundary conditions. In first step, time derivative is discretized by forward difference method. Then, quasilinearization process is used to tackle the non-linearity in the equa...

Purpose
The purpose of this paper is to use the polynomial differential quadrature method (PDQM) to find the numerical solutions of some Burgers'‐type nonlinear partial differential equations.
Design/methodology/approach
The PDQM changed the nonlinear partial differential equations into a system of nonlinear ordinary differential equations (ODEs)....

In this paper, an efficient numerical scheme based on uniform Haar wavelets and the quasilinearization process is proposed for the numerical simulation of time dependent nonlinear Burgers’ equation. The equation has great importance in many physical problems such as fluid dynamics, turbulence, sound waves in a viscous medium etc. The Haar wavelet b...

The two point boundary value problems with Neumann and mixed Robbin’s boundary conditions have great importance in chemical engineering, deﬂection of beams etc. It is not easy task to solve numerically such type of problems. In this paper, Galerkin-ﬁnite element method is proposed for the numerical
solution of the boundary value problem having mixe...

In chemical engineering, deflection of beams and other area of engineering the two point boundary value problems with Neumann and mixed Robbinâ€™s boundary conditions have great importance. It is not an easy task to solve numerically such type of problems. In this paper, we apply Galerkin-finite element method on the considered problem. The problem...

During the past few decades, the idea of using differential quadrature methods for numerical solutions of partial differential equations (PDEs) has received much attention throughout the scientific community. In this article, we proposed a numerical technique based on polynomial differential quadrature method (PDQM) to find the numerical solutions...

In this article, we proposed a numerical technique based on polynomial differential quadrature method (PDQM) to find the numerical solutions of two dimensional hyperbolic telegraph equation with Dirichlet and Neumann boundary condition. The PDQM reduced the problem into a system of second order linear differential equation. Then, the obtained syste...

In this paper, the coupled viscous Burgers’ equations have been solved by using the differential quadrature method. Two test problems considered by different researchers have been studied to demonstrate the accuracy and utility of the present method. The numerical results are found to be in good agreement with the exact solutions. The maximum absol...

In this paper, we develop a numerical scheme based on differential quadrature method to solve nonlinear generalizations of the Fisher and Burgers’ equations with the zero flux on the boundary. In construction of the numerical scheme, quasilinearization is used to tackle the nonlinearity of the problem, which is followed by semi-discretization for s...

In this article, Galerkin-finite element method is proposed to find the numerical solutions of advection-diffusion equation. The equation is generally used to describe mass, heat, energy, velocity, vorticity etc. As test problem, three different solutions of advection-diffusion equation are chosen. Maximum errors norm are calculated and found that...

In this paper, polynomial based differential quadrature method (DQM) is applied for the numerical solution of a class of two-dimensional initial-boundary value problems governed by a non-linear system of partial differential equations. The system is known as the reaction–diffusion Brusselator system. The system arises in the modeling of certain che...

In this paper, a rapid, convergent and accurate differential quadrature method (DQM) is employed for numerical study of a two-dimensional reaction-diffusion Brusselator system. In the Brusselator system the reaction terms arise from the mathematical modeling of chemical systems such as in enzymatic reactions, and in plasma and laser physics in mult...

In this article, we present a numerical scheme for solving sin-gularly perturbed (i.e. highest -order derivative term multiplied by small parameter) Burgers-Huxley equation with appropriate initial and bound-ary conditions. Most of the traditional methods fail to capture the effect of layer behavior when small parameter tends to zero. The presence...

Purpose – The purpose of this paper is to propose a numerical method to solve time dependent Burgers' equation with appropriate initial and boundary conditions. Design/methodology/approach – The presence of the nonlinearity in the problem leads to severe difficulties in the solution approximation. In construction of the numerical scheme, quasilinea...

In this paper we propose a rapid convergent differential quadrature method (DQM) for calculating the numerical solutions of nonlinear two-dimensional Burgers' equations with appropriate initial and boundary conditions. The two dimensional Burgers' equations arise in various kinds of phenomena such as a mathematical model of turbulence and the appro...

In this paper, we study the numerical solutions of Fisher's equation and to a nonlinear diffusion equation of the Fisher type by differential quadrature method. Fisher's equation combines diffusion with logistic nonlinearity. The equation occurs in logistic population growth models, neurophysiology and nuclear reactions. Therefore, numerical study...

A finite element method for the solution of a fourth-order integro-differential equation used to model static deflection in a suspension bridge was given in (Semper 1993). In the present work, a spectral method is given to solve this fourth-order integro-differential equation. The resulting system of equations is solved by Gauss-Jacobi Iterative me...

In this paper, we propose a differential quadrature method for calculating the numerical solutions of nonlinear one-dimensional Berger-Huxley equation with appropriate initial and boundary conditions. Two test problems considered by different researchers have been studied to demonstrate the accuracy and utility of the present method. Solutions obta...

## Projects

Projects (4)

The project aims at numerical analysis and computational modeling of non-linear parabolic mathematical models (3D and higher dimensional ) with singular and variable coefficients that occur in physical, chemical and biological phenomena and engineering sciences. Non-linear parabolic models with singular and variable coefficients find applications in various fields. Also, the research on obtaining analytic and numerical solutions to such models are trending up. These solutions provide information on the physical behavior and other physical parameters of the non-linear phenomena.

To find exact and numerical solutions of some nonlinear partial differential equations