Algorithms based on DQM with new sets of base functions for solving parabolic partial differential equations in $(2+1)$ dimension
Abstract
This paper deals with the numerical computations of two space dimensional time dependent parabolic partial differential equations by adopting adopting an optimal five stage fourth-order strong stability preserving Runge Kutta (SSP-RK54) scheme for time discretization, and three methods of differential quadrature with different sets of modified B-splines as base functions, for space discretization: namely i) mECDQM: (DQM with modified extended cubic B-splines); ii) mExp-DQM: DQM with modified exponential cubic B-splines, and iii) MTB-DQM: DQM with modified trigonometric cubic B-splines. Specially, we implement these methods on convection-diffusion equation to convert them into a system of first order ordinary differential equations,in time which can be solved using any time integration method, while we prefer SSP-RK54 scheme. All the three methods are found stable for two space convection-diffusion equation by employing matrix stability analysis method. The accuracy and validity of the methods are confirmed by three test problems of two dimensional convection-diffusion equation, which shows that the proposed approximate solutions by any of the method are in good agreement with the exact solutions.
Keywords
Cite
@article{arxiv.1611.08057,
title = {Algorithms based on DQM with new sets of base functions for solving parabolic partial differential equations in $(2+1)$ dimension},
author = {Brajesh Kumar Singh and Pramod Kumar},
journal= {arXiv preprint arXiv:1611.08057},
year = {2024}
}