Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5775660 | Applied Mathematics and Computation | 2017 | 8 Pages |
This paper is devoted to giving a rigorous numerical analysis for a fractional differential equation with order αâ¯ââ¯(0, 1). First the fractional differential equation is transformed into an equivalent Volterra integral equation of the second kind with a weakly singular kernel. Based on the aâpriori information about the exact solution, an integral discretization scheme on an aâpriori chosen adapted mesh is proposed. By applying the truncation error estimate techniques and a discrete analogue of Gronwall's inequality, it is proved that the numerical method is first-order convergent in the discrete maximum norm. Numerical results indicate that this method is more accurate and robust than finite difference methods when α is close to 0.