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Analytical and numerical solutions of the Fitzhugh–Nagumo equation and their multistability behavior
Author(s) -
İnan Bilge,
Ali Khalid K.,
Saha Asit,
Ak Turgut
Publication year - 2021
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22516
Subject(s) - quasiperiodic function , multistability , mathematics , forcing (mathematics) , mathematical analysis , traveling wave , exponential function , physics , quantum mechanics , nonlinear system
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.