Numerical solution of space fractional diffusion equation by the method of lines and splines

Younes Salehi, Mohammad T. Darvishi and William E. Schiesser

Applied Mathematics and Computation, 2018, vol. 336, issue C, 465-480

Abstract: This paper is devoted to the application of the method of lines to solve one-dimensional diffusion equation where the classical (integer) second derivative is replaced by a fractional derivative of the Caputo type of order α less than 2 as the space derivative. A system of initial value problems approximates the solution of the fractional diffusion equation with spline approximation of the Caputo derivative. The result is a numerical approach of order O(Δx2+Δtm), where Δx and Δt denote spatial and temporal step-sizes, and 1 ≤ m ≤ 5 is an integer which is set by an ODE integrator that we used. The convergence and numerical stability of the method are considered, and numerical tests to investigate the efficiency and feasibility of the scheme are provided.

Keywords: Space fractional diffusion equation; Caputo derivative; Robin boundary condition; Method of lines; Spline approximation; BDF method (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:336:y:2018:i:c:p:465-480

DOI: 10.1016/j.amc.2018.04.053

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