A Multipole algorithm for solving a fractional generalization of the helmholtz equation





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.

Author Biography

N.S. Belevtsov


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How to Cite

Белевцов Н. A Multipole Algorithm for Solving a Fractional Generalization of the Helmholtz Equation // Numerical Methods and Programming (Vychislitel’nye Metody i Programmirovanie). 2021. 22. 109-120. doi 10.26089/NumMet.v22r208



Methods and algorithms of computational mathematics and their applications