Eurasian Journal of Mathematical Theory and Computer Sciences 4-jild 6-son (2024) · 20–27-betlar

SOLUTION OF THE NEUMANN PROBLEM FOR THE LAPLACE EQUATION IN A RECTANGLE BY THE FOURIER METHOD

Bogdan, Anna

DOI: 10.5281/zenodo.12069655 · Manbada o'qish → · PDF (manba serverida)

Annotatsiya

The presented article discusses the Fourier method of separation of variables for solving the Laplace equation in a rectangular domain with Neumann boundary conditions. The main stages of this method are subsequently revealed: Representation of the general solution of the Laplace equation in a rectangular domain using Fourier series. Satisfying the Neumann boundary conditions using Fourier series. Constructing the solution of the Neumann problem, including the expansion of the boundary functions into Fourier series, determining the Fourier coefficients, and writing the final solution in the form of a Fourier series. Analysis of the properties of the obtained solution, including its uniqueness, smoothness, continuity, and physical interpretation.

Laplace's equation, stationary states, physical fields, heat conduction, electrostatics, magnetostatics, diffusion, hydrodynamic flows, harmonicity, infinite differentiability, maximum principle, boundary conditions, uniqueness of solution.

Metadata manbasi: jurnal OAI-PMH arxivi · Sindex to'liq matnni saqlamaydi, manbaga havola beradi.