Numerical solution of the Burgers' equation over geometrically graded mesh

Abstract

Purpose

The purpose of this paper is to illustrate how the numerical solution of the Burgers' equation is obtained using the methods of cubic B‐spline collocation and quadratic B‐spline Galerkin over the geometrically graded mesh.

Design/methodology/approach

The spatial domain is partitioned into geometrically graded mesh. The finite element methods are constructed within the Galerkin and collocation methods using an expansion of the quadratic and cubic B‐splines as an approximate function, respectively, over this mesh.

Findings

When the higher errors are observed at near boundaries for shock‐like and travelling wave solutions of the Burgers' equation, accuracy of the defined methods increase by using finer mesh at near this boundary.

Originality/value

Over the geometrically graded mesh definitions of the quadratic B‐spline Galerkin and cubic B‐spline collocation are given.

Citation

Dağ, İ. and Şahin, A. (2007), "Numerical solution of the Burgers' equation over geometrically graded mesh", Kybernetes, Vol. 36 No. 5/6, pp. 721-735. https://doi.org/10.1108/03684920710749794