Application of Haar-scale-3 wavelet collocation method to the solution of Fitzhugh–Nagumo non-linear partial differential equation
Sonia Arora, Ratesh Kumar · Research in Mathematics · 2025
This paper proposes Scale-3 Haar wavelet collocation methods as one of the recent innovations in analysing the specific class of parabolic Fitzhugh–Nagumo second-order nonlinear partial differential equations within reaction-diffusion systems. Making use of scale-3 Haar wavelets for approximating both space and time derivatives, such a method collocation to the discretization of the space and time variables to derive either implicit or explicit analytical models. Numerical problems concerning nonlinearities as well as crucial source terms with varied complexities, where the validity of the algorithm had to be extensively tested through stringent tests at high accuracy level. Results for graphical presentation display its impressive high-precision potential when using minimum numbers of collocation points are discussed. Furthermore, the approach opens doors to promising perspectives in dealing with a variety of nonlinear partial differential equations, thus establishing it as one of the versatile tools in high-level mathematical modelling and applied sciences. Scalability and adaptability make it relevant for applications much wider than to reaction-diffusion systems alone.