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Method of Non-orthogonal Series

In: Methods of Mathematical Physics

Author

Listed:
  • 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)

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.

Suggested Citation

  • Alexey N. Karapetyants & Vladislav V. Kravchenko, 2022. "Method of Non-orthogonal Series," Springer Books, in: Methods of Mathematical Physics, chapter 0, pages 377-384, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-17845-0_15
    DOI: 10.1007/978-3-031-17845-0_15
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