Article ID Journal Published Year Pages File Type
10418002 Journal of Applied Mathematics and Mechanics 2005 7 Pages PDF
Abstract
An algorithm for constructing a general solution of an oscillatory system without determining the eigenvectors, which are the main source of the computational instability of classical methods, is proposed and justified. Souriau's algorithm [1-3], developed for solving systems of linear algebraic equations, is extended to the construction of a general solution of systems of linear ordinary differential equations. The adjoint matrix, consisting of the cofactors of the elements of the initial matrix, and the representation of the characteristic polynomial in terms of the characteristic adjoint matrix, play an important role here. the algorithm consists of simple algebraic operations, in addition to the numerical integration of a single differential equation, called the characteristic equation.
Related Topics
Physical Sciences and Engineering Engineering Mechanical Engineering
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