Orthogonal polynomials

Machine learning

Chebyshev pseudospectral method

Chebyshev polynomials

Mathematical analysis

Chebyshev equation

Fractional calculus

Real interest rate

Economics

Chebyshev nodes

Interest rate

Collocation method

Chebyshev filter

Classical orthogonal polynomials

Spectral method

Convergence (economics)

Applied mathematics

Mathematics

Computer science

Numerical analysis

Economic growth

Ordinary differential equation

Monetary economics

Fisher equation

Differential equation

Collocation (remote sensing)

Chaos Solitons & Fractals

In this paper, an efficient numerical method is introduced for solving the fractional (Caputo sense) Fisher equation. This equation presents the problem of biological invasion and occurs, e.g., in ecology, physiology, and in general phase transition problems and others. We use the spectral collocation method which is based upon Chebyshev approximations. The properties of Chebyshev polynomials are utilized to reduce the proposed problem to a system of ODEs, which is solved by using finite difference method (FDM). Some theorems about the convergence analysis are stated. A numerical simulation and a comparison with the previous work are presented. We can apply the proposed method to solve other problems in engineering and physics.

A numerical approach for solving the fractional Fisher equation using Chebyshev spectral collocation method