Numerical integration of nonlinear FitzHugh-Nagumo Partial Differential Equations using second derivative two-step hybrid algorithm

Abstract

This manuscript presents a second derivative two-step hybrid block method derived through collocation techniques. The derived scheme and the sixth order compact difference schemes are used to efficiently solve the nonlinear FitzHugh-Nagumo Partial Differential Equations (PDE). The sixth order standard compact difference schemes are used to semi-discretize the nonlinear FitzHugh PDE to a first-order system of ordinary differential equations (ODE). The derived two-step hybrid block scheme profer approximate solution to the resulting system of ODEs. The analysis of the derived hybrid methods are shown. The numerical results reveal that the derived block scheme is efficient and effective for solving FitzHugh-Nagumo PDE.

AMS Subject Classification: 65M06, 65N35, 35F50