Highly accurate collocation methodology for solving the generalized Burgers–Fisher’s equation

An improvised collocation scheme is applied for the numerical treatment of the nonlinear generalized Burgers–Fisher’s (gBF) equation using splines of degree three. In the proposed methodology, some subsequent rectifications are done in the spline interpolant, which resulted in the magnification of the order of convergence along the space direction. A finite difference approach is followed to integrate the time direction. Von Neumann methodology is opted to discuss the stability of the method. The error bounds and conver-gence study show that the technique has (s۴ + ∆t۲) order of convergence. The correspondence between the approximate and analytical solutions is shown by graphs, plotted using MATLAB and by evaluating absolute error.

Keywords:

Generalized Burgers–Fisher’s equation , cubic B-splines , Collo-cation method , Finite difference scheme , Green’s function , von Neumann analysis