Analytic Solution for Two-Dimensional Heat Equation for an Ellipse Region

Abstract

In this study, an altenative method is presented for the solution of two-dimensional heat equation in an ellipse region. In this method, the solution function of the problem is based on the Green, and therefore on elliptic functions. To do this, it is made use of the basic consepts associated with elliptic integrals, conformal mappings and Greenfunctions.

Bernstein Series Solution of the Heat Equation in 2-D

“…Solution of the two-dimensional heat equation in a square region was given by Kurt [11]. Analytic solution was given two-dimensional heat equation for some regions by Baykuş Savaşaneril et al [2,3,5,7]. The Chebyshev tau technique for the solution of Laplace's equation [1] and Chebyshev tau matrix method for Poisson-type equations in irregular domain [8] were studied by Ahmadi et al and Kong et al Error analysis of the Chebyshev collocation method for linear second-order partial differential equations was expressed by Yüksel et al [13,14,15].…”