A Review on Higher Order Spline Techniques for Solving Burgers Equation using B-Spline methods and Variation of B-Spline Techniques

TL;DR

This paper reviews higher order B-spline and variation of B-spline methods for numerically solving Burgers' equation, comparing their efficiency, stability, and effectiveness through various schemes and techniques.

Contribution

It provides a comprehensive comparison and analysis of multiple B-spline based techniques for Burgers' equation, highlighting their advantages and computational performance.

Findings

B-spline methods effectively solve Burgers' equation with good stability.

Quadratic and cubic B-spline Galerkin methods show high accuracy.

Variation of B-spline techniques offer computational advantages.

Abstract

This is a summary of articles based on higher order B-splines methods and the variation of B-spline methods such as Quadratic B-spline Finite Elements Method, Exponential Cubic B-Spline Method Septic B-spline Technique, Quintic B-spline Galerkin Method, and B-spline Galerkin Method based on the Quadratic B-spline Galerkin method (QBGM) and Cubic B-spline Galerkin method (CBGM). In this paper we study the B-spline methods and variations of B-spline techniques to find a numerical solution to the Burgers' equation. A set of fundamental definitions including Burgers equation, spline functions, and B-spline functions are provided. For each method, the main technique is discussed as well as the discretization and stability analysis. A summary of the numerical results is provided and the efficiency of each method presented is discussed. A general conclusion is provided where we look at a comparison between the computational results of all the presented schemes. We describe the effectiveness and advantages of these methods