Cubic B-spline collocation method on a non-uniform mesh for solving nonlinear parabolic partial differential equation

In this paper, an approximate solution of a nonlinear parabolic partial differential equation is obtained for a non-uniform mesh. The scheme for partial differential equation subject to Neumann boundary conditions is based on cubic B-spline collocation method. Modified cubic B-splines are proposed over non-uniform mesh to deal with the Dirichlet boundary conditions. This scheme produces a system of first order ordinary differential equations. This system is solved by Crank Nicholson method. The stability is also discussed using Von Neumann stability analysis. The accuracy and efficiency of the scheme are shown by numerical experiments. We have compared the approximate solutions with that in the literature.

Keywords:

Nonlinear parabolic partial differential equation , Collocation method , Cubic B-spline , Non-uniform mesh , Crank-Nicolson method