Convergence of the matrix transformation method for the finite difference approximation of fractional order diffusion problems

Institute of Mathematics, Czech Academy of Sciences - Tập 62 Số 1 - Trang 15-36 - 2017
Szekeres, Béla J.1, Izsák, Ferenc2
1MTA-ELTE Numnet Research Group, Eötvös Loránd University, Budapest, Hungary
2Department of Applied Analysis and Computational Mathematics, MTA-ELTE Numnet Research Group, Eötvös Loránd University, Budapest, Hungary

Tóm tắt

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 R2 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 approximations of fractional order derivatives. The spatial convergence of this method is proved and demonstrated by some numerical experiments.

Tài liệu tham khảo

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