关键词: parabolic equation, difference schemes, error estimate, stability

Abstract: The present paper is to introduce the method for the calculation of the roof with orthotropic shallow conoidal shells which are always used in the industrial buildings. Since the middle surface of the shallow conoidal shell having the variable curvatures and twists, therefore the system of fundamental equations, which are obtained by us, are being possessed of the variable coefficients.If we want to find the exact analytical solutions, it will be involved in great mathematical difficulties. This paper gives the approximate solutions of the orthotropic shallow conoidal shell roof which is simply supported at all edges and under the uniformly distributed load. In this paper the method of small parameter is used.

Key words: parabolic equation, difference schemes, error estimate, stability