Geodesic
Convergence of the matrix transformation method for the finite difference approximation of fractional order diffusion problems
Applications of Mathematics, Tome 62 (2017) no. 1, pp. 15-36

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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 $\mathbb {R}^2$ 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 approximations of fractional order derivatives. The spatial convergence of this method is proved and demonstrated by some numerical experiments.
DOI : 10.21136/AM.2017.0385-15
Classification : 35R11, 65M06, 65M12
Keywords: fractional diffusion problem; finite differences; matrix transformation method 
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Szekeres, Béla J.; Izsák, Ferenc. Convergence of the matrix transformation method for the finite difference approximation of fractional order diffusion problems. Applications of Mathematics, Tome 62 (2017) no. 1, pp. 15-36. doi: 10.21136/AM.2017.0385-15

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