Convergence of the matrix transformation method for the finite difference approximation of fractional order diffusion problems
Béla J. Szekeres, Ferenc Izsák (2017)
Applications of Mathematics
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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 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...