Convolution quadrature time discretization of fractional diffusion-wave equations

Cuesta, Eduardo; Lubich, Christian; Palencia, Cesar

doi:10.1090/S0025-5718-06-01788-1

Convolution quadrature time discretization of fractional diffusion-wave equations
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by Eduardo Cuesta, Christian Lubich and Cesar Palencia PDF

Math. Comp. 75 (2006), 673-696 Request permission

Abstract:

We propose and study a numerical method for time discretization of linear and semilinear integro-partial differential equations that are intermediate between diffusion and wave equations, or are subdiffusive. The method uses convolution quadrature based on the second-order backward differentiation formula. Second-order error bounds of the time discretization and regularity estimates for the solution are shown in a unified way under weak assumptions on the data in a Banach space framework. Numerical experiments illustrate the theoretical results.

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