Numerical method with fractional splines for a subdiffusion problem

摘要

We consider a subdiffusion problem described by a time fractional Riemann-Liouville derivative of order 0 a 1. The main purpose of this work is to show how we can apply fractional splines of order 0 ss = 1 to approximate a fractional integral and hence how to solve the subdiffusion problem using this approach. To discuss the convergence of the numerical method we present the error bounds for the fractional splines and the fractional integral approximations and study the von Neumann stability analysis. We observe that, depending on the smoothness of the solution, the order of convergence will be affected by the values of a and ss. Numerical tests are presented along thework to highlight several properties of the fractional splines and the numerical tests in the end illustrate the performance of the numerical method.