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 some well-known problems for the Burgers' equation.

Quartic trigonometric B-spline algorithm for numerical solution of the regularized long wave equation

“…Abbas et al proposed a collocation finite difference scheme based on cubic trigonometric B-spline for the numerical solution of a one-dimensional hyperbolic equation (wave equation) with the nonlocal conservation condition [1]. Burgers' equation was solved by the collocation method using the cubic trigonometric B-spline and the subdomain Galerkin method using the quadratic trigonometric B-spline, respectively, in [2,5]. The cubic and quadratic trigonometric B-spline Galerkin finite element methods were proposed for the numerical solution of the RLW equation by Irk and Keskin [13,14].…”