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JOURNALS // Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki // Archive

Zh. Vychisl. Mat. Mat. Fiz., 2024 Volume 64, Number 11, Pages 2155–2159 (Mi zvmmf11870)

Partial Differential Equations

Analogue of Poisson’s formula for the solution of the Helmholtz equation

A. O. Savchenko

Institute of Computational Mathematics and Mathematical Geophysics of Siberian Branch of Russian Academy of Sciences, 630090, Novosibirsk, Russia

Abstract: The paper presents analogues of Poisson’s formula for solving interior and exterior boundary value problems with Dirichlet or Neumann boundary conditions on a sphere for the Helmholtz equation, with the kernels of the integrals in the form of series.

Key words: Helmholtz equation, spherical harmonics, boundary value problems for a sphere, Laplace formula.

UDC: 519.632

Received: 16.05.2024
Revised: 16.05.2024
Accepted: 06.07.2024

DOI: 10.31857/S0044466924110106


 English version:
Computational Mathematics and Mathematical Physics, 2024, 64:11, 2666–2671

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© Steklov Math. Inst. of RAS, 2025