A nonpolynomial collocation method for fractional terminal value problems

作者：Ford N J; Morgado M L^*; Rebelo M

来源：Journal of Computational and Applied Mathematics, 2015, 275: 392-402.

DOI：10.1016/j.cam.2014.06.013

• Fractional calculus
• Caputo derivative
• Boundary value problem
• Nonpolynomial collocation method

In this paper we propose a nonpolynomial collocation method for solving a class of terminal (or boundary) value problems for differential equations of fractional order alpha, 0 < alpha < 1. The approach used is based on the equivalence between a problem of this type and a Fredholm integral equation of a particular form. Taking into account the asymptotic behaviour of the solution of this problem, we propose a nonpolynomial collocation method on a uniform mesh. We study the order of convergence of the proposed algorithm and a result on optimal order of convergence is obtained. In order to illustrate the theoretical results and the performance of the method we present several numerical examples.

• 出版日期2015-2