Open AccessOn the numerical solution of Fisher's equation by an efficient algorithm based on multiwavelets
Author(s) -
Haifa Bin Jebreen
Publication year - 2020
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2021144
Subject(s) - mathematics , discretization , ode , ordinary differential equation , galerkin method , stability (learning theory) , algorithm , convergence (economics) , wavelet , interval (graph theory) , rate of convergence , finite difference method , differential equation , finite element method , mathematical analysis , computer science , key (lock) , physics , computer security , combinatorics , machine learning , artificial intelligence , economic growth , economics , thermodynamics
In this work, we design, analyze, and test an efficient algorithm based on the finite difference method and wavelet Galerkin method to solve the well known Fisher's equation. We employed the Crank-Nicolson scheme to discretize the time interval into a finite number of time steps, and this gives rise to an ordinary differential equation at each time step. To solve this ODE, we utilize the multiwavelets Galerkin method. The $ L^2 $ stability and convergence of the scheme have been investigated by the energy method. Illustrative examples are provided to verify the efficiency and applicability of the method.