Article ID Journal Published Year Pages File Type
8902067 Journal of Computational and Applied Mathematics 2018 12 Pages PDF
Abstract
In this paper a two-point boundary value problem with a Caputo fractional derivative is considered. By using a shooting method based on the secant iterative method, the boundary value problem is turned into an initial value problem. Then the initial value problem is transformed into an equivalent integral-differential equation with a weakly singular kernel. An integral discretization scheme on the uniform mesh is developed to approximate the integral-differential equation. By applying the truncation error estimate techniques and a discrete analogue of Gronwall's inequality, it is proved that the numerical scheme is first-order convergent in the discrete maximum norm. Numerical experiments verify the theoretical results.
Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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