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This work considers the solution of the Dirichletproblem for the Laplace equation in the case when the domain is bounded by a circle. The Laplace equation and its basic properties are introduced, and the transition to polar coordinates is carried out. The formulation of the Dirichlet problem on a circlewith given boundary conditions is presented. The method of solving this problem using trigonometric series and the Fourier series to satisfy the boundary conditions is described. Specific examples of solving the Dirichlet problem on a circle with illustrations and numerical results are provided. In conclusion, the importance and practical significance of the obtained solutions for various applied problems are emphasized

  • O'qishlar soni 46
  • Nashr sanasi 01-06-2024
  • Asosiy tilIngliz
  • Sahifalar239-248
English

This work considers the solution of the Dirichletproblem for the Laplace equation in the case when the domain is bounded by a circle. The Laplace equation and its basic properties are introduced, and the transition to polar coordinates is carried out. The formulation of the Dirichlet problem on a circlewith given boundary conditions is presented. The method of solving this problem using trigonometric series and the Fourier series to satisfy the boundary conditions is described. Specific examples of solving the Dirichlet problem on a circle with illustrations and numerical results are provided. In conclusion, the importance and practical significance of the obtained solutions for various applied problems are emphasized

Muallifning F.I.Sh. Lavozimi Tashkilot nomi
1 Bogdan A.M. Student Fergana State University
Havola nomi
1 1."Methods of mathematical physics" -M.A. Lavrentiev, B.V. Shabbat (Chapter 21. Dirichletproblem for Laplace's equation).2."Equations of mathematical physics" -A.N. Tikhonov, A.A. Samarsky (Chapter 2. Dirichlet problem for Laplace’s equation).3."Partial derivatives of mathematical physics equations" -O.A. Ladyzhenskaya, V.A. Solonnikov, N.N. Uraltsev (Chapter 1. Dirichlet problem for Laplace’s equation).4.Goryunov A.F. Equations of mathematical physics in examples and problems. Part 2: Tutorial. -M.: MEPhI, 2008. -528 p.5.Budak B.N., Samarsky A.A., Tikhonov A.N. Collection of problems in mathematical physics. -M.: Fizmatlit, 2003.6.Vladimirov V.S., Zharinov V.V. Equations of mathematical physics. -M.: Fizmatlit, 2003.7.Godunov S.K., Zolotareva E.V. Collection of problems on the equations of mathematical physics. -Novosibirsk: Science, 19748.Koshlyakov N.S., Glinner E.B., Smirnov M.M. Partial differential equations of mathematical physics. -M.: Higher School, 1970.9.Kudryavtsev L.D. Course of mathematical analysis t 1.2. -M.: Bustard, 2006.10.Lebedev N.N., Skalskaya I.P., Uflyand Ya.S. Collectionof problems in mathematical physics. -M.: Gostekhizdat, 1955.11.Smirnov M.M. Problems on the equations of mathematical physics. -M.: Nauka, 197512.Tikhonov A.N., Samarsky A.A. Equations of mathematical physics. -M.: MSU, Science, 2004.
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