SOLUTION OF THE NEUMANN PROBLEM FOR THE LAPLACE EQUATION IN A RECTANGLE BY THE FOURIER METHOD
Vol. 4 No. 6 (2024): Евразийский журнал математической теории и компьютерных наук 20-27
Abstract
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.
Keywords:
References
Matrosov A.V. Maple 6. Solving problems of higher mathematics and mechanics. – St. Petersburg: BHV-Petersburg, 2001, 528 p.
N. Teshavoeva. Mathematician physics methodology. Fergana. Ukituvchi. 1980.
Matrosov A.V. Maple 6. Solving problems of higher mathematics and mechanics. – St. Petersburg: BHV-Petersburg. – 2001.– 528 p.
Kirsanov M.N. Maple 13 and Maplet. Solving mechanics problems. M.: Fizmatlit, 2010, 349 p.
Galtsov D.V. Theoretical physics for mathematics students. – M.: Publishing house Mosk. University, 2003. – 318 p.
Samarsky A. A., Mikhailov A. P. Mathematical modeling: Ideas. Methods. Examples. — 2nd ed., rev. - M.: Fizmatlit, 2005. - 320 p.
M. Salokhiddinov. Mathematician physics tenglamalari. Tashkent. Uzbekistan. 2002.
M. T. Rabbimov. Mathematics. Tashkent. Fan ziyoshi. 2022. – 285 p.
Goryunov A.F. Equations of mathematical physics in examples and problems. Part 2: Tutorial. - M.: MEPhI, 2008. - 528 p.
Budak B.N., Samarsky A.A., Tikhonov A.N. Collection of problems in mathematical physics. - M.: Fizmatlit, 2003.
Vladimirov V.S., Zharinov V.V. Equations of mathematical physics. - M.: Fizmatlit, 2003.
Godunov S.K., Zolotareva E.V. Collection of problems on the equations of mathematical physics. - Novosibirsk: Science, 1974.
Koshlyakov N.S., Glinner E.B., Smirnov M.M. Partial differential equations of mathematical physics. - M.: Higher School, 1970.
Kudryavtsev L.D. Course of mathematical analysis t 1.2. - M.: Bustard, 2006.
Lebedev N.N., Skalskaya I.P., Uflyand Y.S. Collection of problems in mathematical physics. - M.: Gostekhizdat, 1955.
Smirnov M.M. Problems on the equations of mathematical physics. - M.: Nauka, 1975.
Readership
Downloads
Published
Issue
Section
How to Cite
