Solution of Dirichlet problem for a rectangular region in terms of elliptic functions

Kurt, Nurcan; Sezer, Mehmet; Çelik, Adem

doi:10.1080/0020716042000261441

Cited by 5 publications

(3 citation statements)

References 3 publications

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“…Han and Hasebe [6] also reviewed Green's functions for a point heat source in various thermoelastic boundary value problems for an infinite plane with an inhomogeneity. Green function of the Dirichlet problem for the Laplace differential equation in a rectangular domain was expressed in terms of elliptic functions and the solution of the problem was based on the Green function and therefore on elliptic functions by Kurt et al [7]. Hsiao et al [8] showed an equivalence between the weak solution and the various boundary integral solutions, and described a coupling procedure for an exterior initial boundary value problem for the nonhomogeneous heat equation.…”

Section: Introductionmentioning

confidence: 99%

Solution of the two-dimensional heat equation for a square in terms of elliptic functions

Kurt

2008

Journal of the Franklin Institute

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Section: Introductionmentioning

confidence: 99%

Solution of the two-dimensional heat equation for a square in terms of elliptic functions

Kurt

2008

Journal of the Franklin Institute

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“…The Green function of the Dirichlet problem for the Laplace differential equation in a triangle region was expressed in terms of elliptic functions and the solution of problem was based on the Green function, and therefore on elliptic functions by Kurt and Sezer [9,10]. Solution of the two-dimensional heat equation in a square region was given by Kurt [11].…”

Section: Introductionmentioning

confidence: 99%

Bernstein Series Solution of the Heat Equation in 2-D

Savaşaneril¹

2017

ntmsci

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A broad class of steady-state physical problems can be reduced to finding the harmonic functions that satisfy certain boundary conditions. The Dirichlet problem for the Laplace equation is one of the above mentioned problems. In this paper, a numerical matrix method is developed for numerically solving the Heat equation in 2-D. The method converts the heat equation in 2-D to a matrix equation, which corresponds to a system of linear algebraic equations. Error analysis is included to demonstrate the validity and applicability of the technique. Finally, the effectiveness of the method is illustrated in the heat equation for a cut ring region.

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“…In another study, Han and Hasebe [6] also reviewed Green's functions for a point heat source in various thermoelastic boundary value problems for an infinite plane with an inhomogeneity. Green function of the Dirichlet problem for the Laplace differential equation in a rectangular domain was expressed in terms of elliptic functions and the solution of the problem was based on the Green function and therefore on elliptic functions by Kurtet al [7]. Hsiao and Saranen [8] showed an equivalence between the weak solution and the various boundary integral solutions, and described a coupling procedure for an exterior initial boundary value problem for the nonhomogeneous heat equation.…”

Section: Introductionmentioning

confidence: 99%