Local RBF-FD-Based Mesh-free Scheme for Singularly Perturbed Convection-Diffusion-Reaction Models with Variable Coefficients

Ram Jiwari,Sukhveer Singh,Paramjeet Singh,Antonio Di Crescenzo

doi:10.1155/2022/3119482

Abstract

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, LRBF-FD approximation is used for spatial discretization, and we obtained a system of linear equations. Then, the obtained linear system is solved by LU decomposition method in MATLAB. For numerical simulation, four singularly perturbed models are pondered to check the efficiency and chastity of the proposed scheme.

Highlights

Perturbed models (SPMs) can be seen in different areas of science, medicine, and engineering
We present a mesh-free scheme based on local radial basis function-finite difference (LRBF-FD) approximation for the unsteady-state singularly perturbed CDR models with two parameters and variable coefficients
We will develop a mesh-free scheme based on forward finite difference (FFD) and LRBF-FD for the simulation of parabolic SPMs (1). e steps of the scheme are as follows

Summary

Introduction

Perturbed models (SPMs) can be seen in different areas of science, medicine, and engineering. Singularly perturbed convention diffusion problems are solved by Ahmad and Kalarestaghi [25] using LRBFs methods. These problems are steady state and with constant coefficients. Is motivates the authors to develop LRBF-FD scheme for unsteady-state singularly perturbed CDR models. To achieve this aim, we present a mesh-free scheme based on LRBF-FD approximation for the unsteady-state singularly perturbed CDR models with two parameters and variable coefficients. E novelty of the work is that we solved unsteady-state singularly perturbed problems with two parameters and variable coefficients. Concluding remarks of the work are given in the final Section 6

RBFs and Local RBF-FD Approximation

LRBF-FD Method Formulation

Semidiscretization

Concluding Remarks