On the construction of iterated collocation-type approximations for linear fractional differential equations

Abstract

The present paper is concerned with the numerical solution of initial value problems for linear Caputo-type fractional differential equations. Some regularity results are presented and, using a reformulated integral equation approach, a high-order collocation method and its iterated version are constructed. Global superconvergence results of the iterated version are studied. Numerical examples confirming the theoretical results are also given.