A Multipole algorithm for solving a fractional generalization of the helmholtz equation
Keywords:fractional generalization of Helmholtz equation, fractional Laplacian, fundamental solution, multipole expansion, multipole method, numerical algorithm
The problem of constructing an efficient numerical algorithm for solving a fractional generalization of the Helmholtz equation with the fractional Laplacian is considered. A multipole expansion based on the factorized representation of the fundamental solution of the considered equation is constructed. A numerical method for computing the values of Fox H-functions from the multipole expansion is proposed. A modification of the multipole algorithm for solving the considered fractional generalization of the Helmholtz equation is developed. Numerical results demonstrating the efficiency of the proposed algorithms are discussed.
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