Work

Higher-order approximations for space-fractional diffusion equation

Year: 2024

Type: article

Abstract: Second-order and third-order finite difference approximations for fractional derivatives are derived from a recently proposed unified explicit form. The Crank-Nicholson schemes based on these approximations are applied to discretize the space-fractional diffusion equation. We theoretically analyse the convergence and stability of the Crank-Nicholson schemes, proving that they are unconditionally stable. These schemes exhibit unconditional stability and convergence for fractional derivatives of order in the range . Numerical examples further confirm the convergence order and unconditional stability of the approximations, demonstrating their effectiveness in practice.

Source: Journal of Numerical Analysis and Approximation Theory

DOI: 10.33993/jnaat532-1501

Authors: Anura Gunarathna Wickramarachchi, Haniffa Mohamed Nasir

Institutions: Rajarata University of Sri Lanka, Sultan Qaboos University

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4405531971

FWCI:

Cites: 28

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Related to: 10