شاهرخ اسمعیلی

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.