Travelling wave solution of fourth order reaction diffusion equation using hybrid quintic hermite splines collocation technique

Abstract

Fourth order extended Fisher Kolmogorov reaction diffusion equation has been solved numerically using a hybrid technique. The temporal direction has been discretized using Crank Nicolson technique. The space direction has been split into second order equation using twice continuously differentiable function. The space splitting results into a system of equations with linear heat equation and non linear reaction diffusion equation. Quintic Hermite interpolating polynomials have been implemented to discretize the space direction which gives a system of collocation equations to be solved numerically. The hybrid technique ensures the fourth order convergence in space and second order in time direction. Unconditional stability has been obtained by plotting the eigen values of the matrix of iterations. Travelling wave behaviour of dependent variable has been obtained and the computed numerical values are shown by surfaces and curves for analyzing the behaviour of the numerical solution in both space and time directions.