A higher order numerical scheme for generalized fractional diffusion equations,International Journal for Numerical Methods in Fluids

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A higher order numerical scheme for generalized fractional diffusion equations
International Journal for Numerical Methods in Fluids ( IF 1.7 ) Pub Date : 2020-05-10 , DOI: 10.1002/fld.4852
Qinxu Ding ₁ , Patricia J. Y. Wong ₁

Affiliation

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.

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