An Enriched Radial Point Interpolation - Rosenbrock Method for Numerical Simulation of Fitzhugh-Nagumo Equation

In present study, we proposed an efficient numerical approach forFitzhugh-Nagumo equation which is a nonlinear partial differentialequation and has many applications in various branches of science.The suggested numerical method uses a meshless method called as enrichedradial point interpolation method for discretization of space variableswhich forms a large system of ordinary differential equations (ODEs).In general, the acquired ODEs system is stiff therefore to obtaingood results a small time step size should be used for time integration.In order to put relaxation on the time step size a splitting approachis utilized which divide the equation into non-stiff and stiff terms.Then a Rosenbrock method is devised to solve stiff term and a strongstability preserving Runge Kutta method is proposed to solve non-stiffterm. To show efficiency of the suggested method some numerical testsare fulfilled and acquired results are compared with available numericaltechniques in literature such as collocation, meshless and finitedifference methods, and with exact solution. The comparisons revealaccuracy of the suggested method.