Cubic B‐spline differential quadrature methods and stability for Burgers' equation

Abstract

Purpose

The purpose of this paper is to simulate numerical solutions of nonlinear Burgers' equation with two well‐known problems in order to verify the accuracy of the cubic B‐spline differential quadrature methods.

Design/methodology/approach

Cubic B‐spline differential quadrature methods have been used to discretize the Burgers' equation in space and the resultant ordinary equation system is integrated via Runge‐Kutta method of order four in time. Numerical results are compared with each other and some former results by calculating discrete root mean square and maximum error norms in each case. A matrix stability analysis is also performed by determining eigenvalues of the coefficient matrices numerically.

Findings

Numerical results show that differential quadrature methods based on cubic B‐splines generate acceptable solutions of nonlinear Burgers' equation. Constructing hybrid algorithms containing various basis to determine the weighting coefficients for higher order derivative approximations is also possible.

Originality/value

Nonlinear Burgers' equation is solved by cubic B‐spline differential quadrature methods.

Citation

Korkmaz, A. and Dağ, İ. (2013), "Cubic B‐spline differential quadrature methods and stability for Burgers' equation", Engineering Computations, Vol. 30 No. 3, pp. 320-344. https://doi.org/10.1108/02644401311314312