Construction and analysis of some nonstandard finite difference methods for the <scp>FitzHugh–Nagumo</scp> equation
Koffi Messan Agbavon, Appanah Rao Appadu
Abstract
Abstract In this work, we construct four versions of nonstandard finite difference schemes in order to solve the FitzHugh–Nagumo equation with specified initial and boundary conditions under three different regimes giving rise to three cases. The properties of the methods such as positivity and boundedness are studied. The numerical experiment chosen is quite challenging due to shock‐like profiles. The performance of the four methods is compared by computing L 1 , L ∞ errors, rate of convergence with respect to time and central processing unit time at given time, T = 0.5. Error estimates have also been studied for the most efficient scheme.
Topics & Concepts
MathematicsConvergence (economics)Applied mathematicsBoundary (topology)Rate of convergenceShock (circulatory)Construct (python library)Finite differenceFinite difference methodWork (physics)Mathematical analysisComputer scienceKey (lock)Mechanical engineeringProgramming languageEconomic growthEngineeringComputer securityMedicineInternal medicineEconomicsFractional Differential Equations SolutionsNumerical methods for differential equationsNonlinear Waves and Solitons