Variational Iteration Method for Solving Differential Equations with Piecewise Constant Arguments

Abstract

In this paper, variational iteration method is applied for finding the solution of differential equations with piecewise constant arguments. A correction functional is constructed by a general Lagrange multiplier, which can be identified by variational theory. This technique provides a sequence of functions which converges to the exact solution of the problem without discretization of the variables. The flexibility and adaptation provided by the method have been verified by an example.

The Ensuring of the Economic Security of Industrial Enterprises in the Context of Forming a Flexible Management Model: Prerequisites and Tools

“…However, we must take into account that such a function will depend on the N variables. In addition, although each feature (factor influencing the threat) in our case has a finite set of potential values, the desired function cannot be considered as given on a discrete (and, in fact, finite) lattice set of its arguments [5][6][7]. If it were so, then it would be possible to compile a kind of correspondence table between all the variants of the features lists and conditions, after which the task of classifying the condition according to the list of N features, would solved in a trivial way.…”

“…where the auxiliary function Ψ(x) returns an integer part of the number x. Theoretically, the matrix (5) can have the size N×M, where m=1 and k=j by formula (6). In this case, each sign in each state (degree of threat) will have only one assessment.…”