Trigonometric quadratic B-spline subdomain Galerkin algorithm for the Burgers’ equation

Abstract

A variant of the subdomain Galerkin method has been set up to find numerical solutions of the Burgers’ equation. Approximate function consists of the combination of the trigonometric B-splines. Integration of Burgers’ equation has been achived by aid of the subdomain Galerkin method based on the trigonometric B-splines as an approximate functions. The resulting first order ordinary differential system has been converted into an iterative algebraic equation by use of the Crank-Nicolson method at successive two time levels. The suggested algorithm is tested on somewell-known problems for the Burgers’ equation.

Keywords

• Burgers’ equation
• Shock and travelling waves
• Subdomain Galerkin method
• Quadratic trigonometric Bsplines
• Crank-Nicolson method