Approximation of the KdVB equation by the quintic B-spline differential quadrature method

Abstract

In this paper, the Korteweg-de Vries-Burgers’ (KdVB) equation is solved numerically by anew differential quadrature method based on quintic B-spline functions. The weightingcoefficients are obtained by semi-explicit algorithm including an algebraic system with fivebandcoefficient matrix. The L2 and L∞ error norms and lowest three invariants 1 2 I , I and3 I have computed to compare with some earlier studies. Stability analysis of the method isalso given. The obtained numerical results show that the present method performs better thanthe most of the methods available in the literature.

Keywords

• KdVB equation
• differential quadrature method
• quintic B-splines
• partial differential equation
• stability.