Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8900781 | Applied Mathematics and Computation | 2018 | 16 Pages |
Abstract
This paper is devoted to the application of the method of lines to solve one-dimensional diffusion equation where the classical (integer) second derivative is replaced by a fractional derivative of the Caputo type of order α less than 2 as the space derivative. A system of initial value problems approximates the solution of the fractional diffusion equation with spline approximation of the Caputo derivative. The result is a numerical approach of order O(Îx2+Îtm), where Îx and Ît denote spatial and temporal step-sizes, and 1â¯â¤â¯mâ¯â¤â¯5 is an integer which is set by an ODE integrator that we used. The convergence and numerical stability of the method are considered, and numerical tests to investigate the efficiency and feasibility of the scheme are provided.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Younes Salehi, Mohammad T. Darvishi, William E. Schiesser,