Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5776317 | Journal of Computational and Applied Mathematics | 2017 | 25 Pages |
Abstract
We construct and justify a class of high order methods for the numerical solution of initial and boundary value problems for nonlinear fractional differential equations of the form (Dâαy)(t)=f(t,y(t)) with Caputo type fractional derivatives Dâαy of order α>0. Using an integral equation reformulation of the underlying problem we first regularize the solution by a suitable smoothing transformation. After that we solve the transformed equation by a piecewise polynomial collocation method on a mildly graded or uniform grid. Optimal global convergence estimates are derived and a superconvergence result for a special choice of collocation parameters is established. To illustrate the reliability of the proposed algorithms two numerical examples are given.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Arvet Pedas, Enn Tamme, Mikk Vikerpuur,