Work

An Error Analysis Study for the Distributed-Order Time-Fraction Model Using an Efficient Numerical Method

Year: 2024

Type: article

Abstract: In this paper, we propose a numerical scheme based on the shifted Legendre polynomials for solving the forced Korteweg–de Vries (fKdV) equation including a Caputo fractional operator of a distributed order. To obtain numerical solutions of these types of equations, we derive an operational matrix based on the shifted Legendre polynomials, and using this operational matrix, their equations change to a set of nonlinear algebraic systems. Then, by calculating these systems in the collocation points, we solve systems. Also, convergence and error are investigated in this paper. Finally, several numerical examples to show the applicability of our scheme are displayed.

Source: Fractal and Fractional

DOI: 10.3390/fractalfract8110630

Authors: Saeed Kosari, Hao Guan, MohammadHossein Derakhshan

Institutions: Guangzhou University, Qiannan Normal College For Nationalities

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,069

Funder: National Natural Science Foundation of China