A semi-analytic collocation method for space fractional parabolic PDE

ABSTRACT

This paper has presented a new semi-analytic numerical method for solving multi-point problems for nonlinear singular ordinary differential equations (ODEs) of a high order. The method consists of replacing the original equation by an approximate equation which has an exact analytic solution with a set of free parameters. These free parameters are determined by the use of the collocation procedure. Some examples are given to demonstrate the validity and applicability of the new method and a comparison is made with the existing results. In particular, the singular multi-point boundary value problems (BVPs) with equations of the fourth, fifth and sixth orders are considered. Numerical results show that the proposed method is of high accuracy and is efficient for solving a wide class of the nonlinear singular ODEs. The algorithm of the method is very simple and does not require any specific technique in handling the singularity at the endpoints of the solution domain.

KEYWORDS:

• Space fractional PDE
• Caputo derivative
• numerical solution
• time stepping method
• semi-analytic collocation method

2010 AMS SUBJECT CLASSIFICATION:

• 34A08

Disclosure statement

No potential conflict of interest was reported by the authors.