A Discretization Approach for the Nonlinear Fractional Logistic Equation
Date
2020
Authors
Izadi, Mohammad
Srivastava, H.M.
Journal Title
Journal ISSN
Volume Title
Publisher
Entropy
Abstract
The present study aimed to develop and investigate the local discontinuous Galerkin method for the numerical solution of the fractional logistic differential equation, occurring in many biological and social science phenomena. The fractional derivative is described in the sense of Liouville-Caputo. Using the upwind numerical fluxes, the numerical stability of the method is proved in the L∞ norm. With the aid of the shifted Legendre polynomials, the weak form is reduced into a system of the algebraic equations to be solved in each subinterval. Furthermore, to handle the nonlinear term, the technique of product approximation is utilized. The utility of the present discretization technique and some well-known standard schemes is checked through numerical calculations on a range of linear and nonlinear problems with analytical solutions.
Description
Keywords
logistic differential equation, liouville-caputo fractional derivative, local discontinuous galerkin methods, stability estimate
Citation
Izadi, M., & Srivastava, H. M. (2020). A Discretization Approach for the Nonlinear Fractional Logistic Equation. Entropy, 22(11), 1-17. https://doi.org/10.3390/e22111328.