Geodesic
A Multipole algorithm for solving a fractional generalization of the helmholtz equation
Numerical methods and programming, Tome 22 (2021) no. 2, pp. 109-120

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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.
Keywords: fractional generalization of Helmholtz equation, fractional Laplacian, fundamental solution, numerical algorithm.
Mots-clés : multipole expansion, multipole method 
@article{VMP_2021_22_2_a1,
     author = {N. S. Belevtsov},
     title = {A {Multipole} algorithm for solving a fractional generalization of the helmholtz equation},
     journal = {Numerical methods and programming},
     pages = {109--120},
     publisher = {mathdoc},
     volume = {22},
     number = {2},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2021_22_2_a1/}
}
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N. S. Belevtsov. A Multipole algorithm for solving a fractional generalization of the helmholtz equation. Numerical methods and programming, Tome 22 (2021) no. 2, pp. 109-120. http://geodesic.mathdoc.fr/item/VMP_2021_22_2_a1/