Szekeres, Béla and Izsák, Ferenc (2017) CONVERGENCE OF THE MATRIX TRANSFORMATION METHOD FOR THE FINITE DIFFERENCE APPROXIMATION OF FRACTIONAL ORDER DIFFUSION PROBLEMS. APPLICATIONS OF MATHEMATICS, 62 (1). pp. 15-36. ISSN 1572-9109 (Online)
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Abstract
Numerical solution of fractional order diffusion problems with homogeneous Dirichlet boundary conditions is investigated on a square domain. An appropriate extension is applied to have a well-posed problem on R 2 and the solution on the square is regarded as a localization. For the numerical approximation a finite difference method is applied combined with the matrix transformation method. Here the discrete fractional Laplacian is approximated with a matrix power instead of computing the complicated approxima- tions of fractional order derivatives. The spatial convergence of this method is proved and demonstrated in some numerical experiments.
| Item Type: | Article |
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| Subjects: | Q Science / természettudomány > QA Mathematics / matematika > QA74 Analysis / analízis |
| Depositing User: | Ferenc Izsák |
| Date Deposited: | 07 Oct 2017 19:19 |
| Last Modified: | 07 Oct 2017 19:19 |
| URI: | http://real.mtak.hu/id/eprint/65174 |
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