SOLUTION OF THE NEUMANN PROBLEM FOR THE LAPLACE EQUATION ON A RING
Keywords:
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.Abstract
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.
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- 2024-07-06 (2)
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