This paper presents using a new modified homotopy perturbation method (NHPM) for solving linear and nonlinear systems of differential-algebraic equations (DAEs) of index one or higher index without index reduction. By using this scheme, explicit exact solution is calculated in the form of a convergent power series with easily computable components. Some examples are given to illustrate the simp...

Differential-algebraic equations (DAEs) naturally arise in many applications, but present numerical and analytical difficulties. The index of a DAE is a measure of the degree of numerical difficulty. In general, the higher the index is, the more difficult it is to solve the DAE. Therefore, it is desirable to transform the original DAE into an equivalent DAE with lower index. In this paper, we p...

A regular matrix pencil sE − A and its rank one perturbations are considered. We determine the sets in C ∪ {∞} which are the eigenvalues of the perturbed pencil. We show that the largest Jordan chains at each eigenvalue of sE − A may disappear and the sum of the length of all destroyed Jordan chains is the number of eigenvalues (counted with multiplicities) which can be placed arbitrarily in C∪...

The paper deals with an algebraic semantics for Petri nets, based on a process algebra APC (Algebra of Process Components) by the authors. APC is tailored especially for describing processes in Petri nets. This is done by assigning special variables (called E-variables here) to every place of given Petri net, expressing processes initiated in those places. Algebraic semantics is then given as a...