DOI: https://doi.org/10.26089/NumMet.v22r208

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

Authors

  • N.S. Belevtsov

Keywords:

fractional generalization of Helmholtz equation
fractional Laplacian
fundamental solution
multipole expansion
multipole method
numerical algorithm

Abstract

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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Published

2021-05-17

Issue

Vol. 22 (2021): Issue 2.

Section

Methods and algorithms of computational mathematics and their applications

Author Biography

N.S. Belevtsov

Ufa State Aviation Technical University
• Research Engineer

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