Bernstein Series Solution of the Heat Equation in 2-D

Abstract

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.

Keywords

• Heat equation

Kaynakça

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