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

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

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Eurasian Journal of Mathematical Theory and Computer Sciences

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MAQOLA ANNOTATSIYASI

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:1.Representation of the general solution of the Laplace equation in a rectangular domain using Fourier series.2.Satisfying the Neumann boundary conditions using Fourier series.3.Constructing the solution of the Neumann problem, including the expansion of the boundary functions into Fourier series, determining the Fourier coefficients, andwriting the final solution in the form of a Fourier series.4.Analysis of the properties of the obtained solution, including its uniqueness, smoothness, continuity, and physical interpretation

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# diffusion# boundary conditions# maximum principle# Heat conduction# Laplace's equation# electrostatics# stationary states# physical fields# magnetostatics# hydrodynamic flows# harmonicity# infinite differentiability

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https://eroi.uz/11.0201/A0924-0548

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Foydalanilgan adabiyotlar

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