Since the solutions of the fractional differential equations (FDEs) 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.
A Piecewise Nonpolynomial Collocation Method for Fractional Differential Equations
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received October 12, 2015; final manuscript received May 4, 2017; published online June 16, 2017. Assoc. Editor: Brian Feeny.
- Views Icon Views
- Share Icon Share
- Cite Icon Cite
- Search Site
Esmaeili, S. (June 16, 2017). "A Piecewise Nonpolynomial Collocation Method for Fractional Differential Equations." ASME. J. Comput. Nonlinear Dynam. September 2017; 12(5): 051020. https://doi.org/10.1115/1.4036710
Download citation file:
- Ris (Zotero)
- Reference Manager