An Extended Cubic B-spline Finite Element Method for Solving Generalized Burgers-sher Equation

TL;DR

This paper introduces an extended cubic B-spline finite element collocation method for solving the generalized Burgers-Sher equation, demonstrating its accuracy through comparison with analytical solutions.

Contribution

It develops a novel extended B-spline collocation approach for the generalized Burgers-Sher equation, enhancing numerical solution techniques.

Findings

The method accurately approximates solutions to the generalized Burgers-Sher equation.

Numerical errors are minimized, confirming the method's validity.

The approach effectively solves initial boundary value problems.

Abstract

In this study collocation method based on the extended B-spline functions for the numerical solutions of the Generalized Burhers Fisher equation is set up. The approximate solution of the equation is constructed with the combination of the extended B-splines. Some initial boundary value problems are solved by the proposed method. The accuracy and validity and of the method is demonstrated by measuring the error between the numerical solutions and the analytical solutions, if exist.