Adaptative L1 TE and Predictive

swMATH ID: 32154
Software Authors: Yuste, Santos B.; Quintana-Murillo, J.
Description: The notebook corresponding to this method is Adaptative L1 TE and Predictive.nb: Fast, accurate and robust adaptive finite difference methods for fractional diffusion equations. The computation time required by standard finite difference methods with fixed timesteps for solving fractional diffusion equations is usually very large because the number of operations required to find the solution scales as the square of the number of timesteps. Besides, the solutions of these problems usually involve markedly different time scales, which leads to quite inhomogeneous numerical errors. A natural way to address these difficulties is by resorting to adaptive numerical methods where the size of the timesteps is chosen according to the behaviour of the solution. A key feature of these methods is then the efficiency of the adaptive algorithm employed to dynamically set the size of every timestep. Here we discuss two adaptive methods based on the step-doubling technique. These methods are, in many cases, immensely faster than the corresponding standard method with fixed timesteps and they allow a tolerance level to be set for the numerical errors that turns out to be a good indicator of the actual errors.
Homepage: http://www.eweb.unex.es/eweb/fisteor/santos/filesFDE.html
Dependencies: Mathematica
Keywords: finite difference methods; adaptive methods; fractional diffusion equations; anomalous diffusion; numerical examples; error bounds; algorithm; step-doubling technique
Related Software: FODE; ma2dfc; Fractional Heat Conduction Toolbox; Heat Conduction Toolbox; Matplotlib; LFA; Wesseling; Mathematica
Cited in: 23 Publications

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