A higher order numerical scheme for generalized fractional diffusion equations

• Main Authors: Ding, Qinxu, Wong, Patricia J. Y.
• Other Authors: School of Electrical and Electronic Engineering
• Format: Article
• Language: English
• Published: 2022
• Subjects: Engineering::Electrical and electronic engineering; Diffusion Problem; Generalized Fractional Derivative
• Online Access: https://hdl.handle.net/10356/155154
• Institution: Nanyang Technological University

In this article, we develop a higher order approximation for the generalized fractional derivative that includes a scale function z(t) and a weight function w(t). This is then used to solve a generalized fractional diffusion problem numerically. The stability and convergence analysis of the numerical scheme are conducted by the energy method. It is proven that the temporal convergence order is 3 and this is the best result to date. Finally, we present four examples to confirm the theoretical results.