On the numerical solution of Fisher's equation by an efficient algorithm based on multiwavelets

Haifa Bin Jebreen; Haifa Bin Jebreen

doi:10.3934/math.2021144

AIMS Mathematics

2021, Volume 6, Issue 3: 2369-2384. doi: 10.3934/math.2021144

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Research article

On the numerical solution of Fisher's equation by an efficient algorithm based on multiwavelets

Haifa Bin Jebreen ^,

Department of mathematics, College of science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

Received: 04 October 2020 Accepted: 09 December 2020 Published: 17 December 2020
MSC : 65M60, 65T60, 34D20, 35L20

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.
- wavelet Galerkin method,
- multiwavelets,
- energy method,
- Fisher's equation
Citation: Haifa Bin Jebreen. On the numerical solution of Fisher's equation by an efficient algorithm based on multiwavelets[J]. AIMS Mathematics, 2021, 6(3): 2369-2384. doi: 10.3934/math.2021144

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Abstract

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.

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