Numerical Methods for Partial Differential Equations · 2020 · 33 citations · 24 references
Natural SciencesMathematicsComputational MechanicsDifferential EquationsDynamical SystemsApproximation MethodsComputational DynamicsFinite Difference MethodsNonlinear DynamicsNumerical Methods For Differential EquationsSystems Of Differential EquationsFinite Difference SchemesFitzhugh-nagumo ModelMultistabilityNumerical Computation Of Periodic OrbitsPadé ApproximationQuasiperiodic DynamicsTraveling Wave SolutionsWhitehead Problem
Abstract In this paper, we propose an analytical method and a modification of explicit exponential finite difference method (EEFDM) for analytical and numerical solutions of the Fitzhugh–Nagumo (FN) and Newell–Whitehead (NW) equations. The method is improved computationally by using the Padé approximation technique. Furthermore, multistability behavior of traveling wave solutions of the FN and NW equations are examined in presence of external forcing. It is observed that there exist coexisting periodic and quasiperiodic orbits for the FN equation, where as only quasiperiodic orbits is observed in case of NW equation.
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