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The European Physical Journal Special Topics

, Volume 222, Issue 8, pp 1987–1998 | Cite as

A finite difference method with non-uniform timesteps for fractional diffusion and diffusion-wave equations

  • J. Quintana-Murillo
  • S. B. Yuste
Regular Article

Abstract

An implicit finite difference method with non-uniform timesteps for solving fractional diffusion and diffusion-wave equations in the Caputo form is presented. The non-uniformity of the timesteps allows one to adapt their size to the behaviour of the solution, which leads to large reductions in the computational time required to obtain the numerical solution without loss of accuracy. The stability of the method has been proved recently for the case of diffusion equations; for diffusion-wave equations its stability, although not proven, has been checked through extensive numerical calculations.

Keywords

European Physical Journal Special Topic Fractional Derivative Fractional Calculus Adaptive Method Absorb Boundary Condition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© EDP Sciences and Springer 2013

Authors and Affiliations

  1. 1.Departamento de FísicaUniversidad de ExtremaduraBadajozSpain

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