Method of Non-orthogonal Series

Alexey N. Karapetyants and Vladislav V. Kravchenko
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Alexey N. Karapetyants: Southern Federal University, Institute of Mathematics, Mechanics and Computer Sciences and Regional Mathematical Center
Vladislav V. Kravchenko: Cinvestav-IPN, Campus Queretaro, Department of Mathematics

Chapter Chapter 15 in Methods of Mathematical Physics, 2022, pp 377-384 from Springer

Abstract: Abstract In this chapter, we explain the idea of one of the simplest, direct, and efficient numerical approaches for solving boundary value problems of mathematical physics. The approach is often referred to as the method of discrete sources (see, e.g., Doicu et al. Acoustic and Electromagnetic Scattering Analysis (Academic Press, London, 2000)) or the method of non-orthogonal series (see, e.g., Ilyinski et al., Mathematical Models of Electrodynamics (Vysshaya Shkola, Moscow, 1991) (in Russian)). The idea of the method will be explained on the example of the Dirichlet problem for the Helmholtz equation.

Date: 2022
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DOI: 10.1007/978-3-031-17845-0_15

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