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Shahrokh Esmaeili

Shahrokh Esmaeili

Academic rank: Associate Professor
ORCID:
Education: PhD.
ScopusId: 15834719000
Faculty: Faculty of Science
Address: Department of Mathematics University of Kurdistan
Phone: 08733624133

Research

Title
A piecewise nonpolynomial collocation method for fractional differential equations
Type
JournalPaper
Keywords
fractional differential equations, piecewise nonpolynomial, collocation method
Year
2017
Journal Journal of Computational and Nonlinear Dynamics
DOI
Researchers Shahrokh Esmaeili

Abstract

Since the solutions of the fractional differential equations have unbounded derivatives at zero‎, ‎their numerical solutions by piecewise polynomial collocation method on uniform meshes will lead to poor convergence rates‎. ‎This paper presents a piecewise nonpolynomial collocation method for solving such equations reflecting the singularity of the exact solution‎. ‎The entire domain is divided into several small‎ ‎subdomains‎, ‎and the nonpolynomial pieces are constructed using a block-by-block scheme on each subdomain‎. ‎The method is applied to solve linear and nonlinear fractional differential equations‎. ‎Numerical examples are given and discussed to illustrate the effectiveness of the proposed approach‎.