A Review on Higher Order Spline Techniques for Solving Burgers Equation using B-Spline methods and Variation of B-Spline Techniques
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
Keywords
Cite
@article{arxiv.2208.01092,
title = {A Review on Higher Order Spline Techniques for Solving Burgers Equation using B-Spline methods and Variation of B-Spline Techniques},
author = {Maryam Khazaei Pool and Lori Lewis},
journal= {arXiv preprint arXiv:2208.01092},
year = {2022}
}