A Chebyshev Collocation Approach to Solve Fractional Fisher–Kolmogorov–Petrovskii–Piskunov Equation with Nonlocal Condition

Abstract

We provide a detailed description of a numerical approach that makes use of the shifted Chebyshev polynomials of the sixth kind to approximate the solution of some fractional order differential equations. Specifically, we choose the fractional Fisher–Kolmogorov–Petrovskii–Piskunov equation (FFKPPE) to describe this method. We write our approximate solution in the product form, which consists of unknown coefficients and shifted Chebyshev polynomials. To compute the numerical values of coefficients, we use the initial and boundary conditions and the collocation technique to create a system of equations whose number matches the unknowns. We test the applicability and accuracy of this numerical approach using two examples.

Keywords

• fractional Fisher–Kolmogorov–Petrovskii–Piskunov equation
• collocation scheme
• sixth-kind Chebyshev polynomials
• convergence analysis