Numerical solution of fractional differential equations with a collocation method based on Müntz polynomials

Authors:
Shahrokh Esmaeili;M. Shamsi;Yury Luchko
Affiliations:
Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, No. 424, Hafez Ave. Tehran, Iran;Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, No. 424, Hafez Ave. Tehran, Iran;Department of Mathematics II, Technical University of Applied Sciences Berlin, Berlin, Germany
Venue:
Computers & Mathematics with Applications
Year:
2011

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Abstract

This paper presents a computational technique based on the collocation method and Muntz polynomials for the solution of fractional differential equations. An appropriate representation of the solution via the Muntz polynomials reduces its numerical treatment to the solution of a system of algebraic equations. The main advantage of the present method is its superior accuracy and exponential convergence. Consequently, one can obtain good results even by using a small number of collocation points. The accuracy and performance of the proposed method are examined by means of some numerical experiments.