Eurasian Journal of Academic Research 4-jild 6-son (2024) · 249–253-betlar

SOLUTION OF THE NEUMANN PROBLEM FOR THE LAPLACE EQUATION ON A RING

Bogdan, Anna

DOI: 10.5281/zenodo.12072569 · Manbada o'qish → · PDF (manba serverida)

Annotatsiya

This work considers the solution of the Neumann problem on a ring-shaped domain. First, the definition of the domain and the formulation of the Neumann boundary conditions on the inner and outer edges of the ring are provided. To solve the problem, the method of separation of variables in polar coordinates is used. The general solution of the Laplace equation in the ring is obtained, and then, by applying the Neumann boundary conditions, the coefficients in this general solution are determined. As an example, a specific Neumann boundary value problem on a ring is considered, the coefficients in the general solution are calculated, and the final solution is constructed. This work can be useful in the study and solution of partial differential equations in ring-shaped domains.

Laplace's equation, mathematical physics, potential distribution, temperatures, pressures, boundary conditions, Neumann problem, normal derivative, engineering applications, annular region, circular pipes, cylindrical capacitors, theoretical and practical significance.

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