Solution of parabolic PDEs by modified quintic B-spline Crank-Nicolson collocation method

Abstract

In this paper, we present a Crank-Nicolson collocation method based on modified Quintic B-splines for parabolic PDEs. The time-dependent convection–diffusion equation (CDE) and Burgers’ equation are considered. The integration of the problem is handled by using a modified quintic B-spline, over Crank-Nicolson (C-N) scheme, in space. The time-dependent terms are discretized using FDM. The efficiency as well as the accuracy of the method checked through the six numerical examples. The approximate results are presented and compared with the known exact and other numerical solutions. The Von Neumann stability is also performed.

Keywords

• Quintic B-spline basis functions
• Convection-diffusion equation
• Burgers’ equation
• C-N scheme
• Gauss elimination method
• Stability