Efficient Numerical Scheme for Solving (1+1), (2+1)-dimensional and Coupled Burgers Equation

TL;DR

This paper introduces an efficient numerical scheme combining BDF and GDQM for solving 1+1 and 2+1 dimensional Burgers equations, demonstrating high accuracy across different models.

Contribution

The paper develops a novel numerical method integrating BDF and GDQM for Burgers equations in multiple dimensions, enhancing computational efficiency and accuracy.

Findings

High accuracy in absolute error and error norms

Effective for 1D, 2D, and coupled models

Demonstrates computational efficiency

Abstract

A numerical scheme based on backward differentiation formula (BDF) and generalized differential quadrature method (GDQM) has been developed. The proposed scheme has been employed to investigate three cases of Burgers equation, one-dimensional, two-dimensional and two-dimensional coupled models. The results showed an effectiveness accuracy in absolute error and error norms