Stable and Convergent Finite Difference Schemes on NonuniformTime Meshes for Distributed-Order Diffusion Equations
M. Luísa Morgado,
Magda Rebelo,
Luís L. Ferrás
Affiliations
M. Luísa Morgado
Center for Computational and Stochastic Mathematics, Instituto Superior Técnico, University of Lisbon, 1049-001 Lisbon, Portugal
Magda Rebelo
Center for Mathematics and Applications (CMA), Department of Mathematics, NOVA School of Science and Technology, FCT NOVA, Quinta da Torre, 2829-516 Caparica, Portugal
Luís L. Ferrás
Center of Mathematics (CMAT), University of Minho, Campus de Azurém, 4800-058 Guimarães, Portugal
In this work, stable and convergent numerical schemes on nonuniform time meshes are proposed, for the solution of distributed-order diffusion equations. The stability and convergence of the numerical methods are proven, and a set of numerical results illustrate that the use of particular nonuniform time meshes provides more accurate results than the use of a uniform mesh, in the case of nonsmooth solutions.
