Exact Difference Schemes for Multidimensional Heat Conduction Equations

Abstract

-The initial boundary-value problem for the two-dimensional heat conduction equationis considered. A new difference scheme approximating the above equation is constructed. The error of approximation of the considered scheme is O((σ − 0.5)(, where σ is a weight. The main difference between the method proposed in the present paper and the other difference schemes is that for the traveling wave solutions u(x, t) = U 1 2athe considered scheme is exact if the grid steps satisfy definite conditions γ 1 = aτ /h 1 = 1/2, γ 2 = bτ /h 2 = 1/2. The iteration method is used to solve a nonlinear difference equation.

Given a one-step numerical scheme, on which ordinary differential equations is it exact?

“…This condition may apply to either the general solution of the ODE, or only a particular solution (see, for example, Ref. [3]). …”