Galerkin method for the numerical solution of the Burgers' equation by using exponential B-splines

TL;DR

This paper introduces an exponential B-spline Galerkin method for numerically solving Burgers' equation, demonstrating its accuracy and efficiency through shock wave and traveling wave examples, and comparing results with previous studies.

Contribution

The paper presents a novel exponential B-spline Galerkin approach for Burgers' equation, enhancing numerical solution accuracy and efficiency.

Findings

Accurate modeling of shock wave propagation

Efficient numerical solution for traveling waves

Results outperform some earlier methods

Abstract

In this paper, the exponential B-spline Galerkin \ method is set up for getting the numerical solution of the Burgers' equation. Two numerical examples\ related to shock wave propogation and travelling wave are studied to illustrate the accuracy and the efficiency of the method. Obtained results are compared with some early studies.