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A Numerical Method for the Solution of the Time-Fractional Diffusion Equation

Ferrás, L. L.; Ford, N. J.; Morgado, M. Luísa; Rebelo, Magda

Lecture Notes in Computer Science, 8579 (2014), 117-131

In this work we provide a new numerical scheme for the solution of the fractional sub-diffusion equation. This new scheme is based on a combination of a recently proposed non-polynomial collocation method for fractional ordinary differential equations and the method of lines. A comparison of the numerical results obtained with known analytical solutions is carried out, using different values of the order of the fractional derivative and several time and space stepsizes, and we conclude that, as in the fractional ordinary differential equation case, the convergence order of the method is independent of the order of the time derivative and does not decrease when dealing with certain nonsmooth solutions.