Mathematical modeling of complex structures and nonlinear differential equations with movable points

Abstract

Mathematical modeling as one of the strict methods of research justification is applied in different fields of human activity including structural mechanics. Differential equations represent one of the variants of the basics of a mathematical model. If linear differential equations do not cause difficulties, the nonlinear ones will present a serious problem for a researcher due to the appearance of movable singular points. Such differential equations are related to the class of equations generally not solvable in quadratures. This fact actualizes the problem of the approximate methods development to solve this category of equations, since the existing classical methods are very often turned out to be ineffective. This paper presents the development of an analytical method for approximate solutions of nonlinear differential equations with movable singular points. The formulation of the emerged tasks is given as well as the technique of their solution. The obtained theoretical material is tested by numerical experiments confirming the reliability of the results.