In this study‎, ‎an efficient method is presented for solving infinite boundary integro-differential equations (IBI-DE) of the second kind with degenerate kernel in terms of Laguerre polynomials‎. ‎Properties of these polynomials and operational matrix of integration are first presented‎. ‎These properties are then used to transform the integral equation to a matrix equation which corresponds t...

In this paper we deene two compositional net semantics for the stochastic process algebra Markovian Process Algebra (MPA), based on a class of stochastic Petri nets. The rst semantics is operational in style and is deened by structural induction. We prove that both the functional and performance interleaving semantics are retrievable: given a process term E, the reachability graph and the Marko...

In this paper, a new shifted ultraspherical wavelets operational matrix of derivatives is introduced. The two wavelets operational matrices, namely Legendre and first kind Chebyshev operational matrices can be deduced as two special cases. Two numerical algorithms based on employing the shifted ultraspherical wavelets operational matrix of derivatives for solving linear and nonlinear differenti...

Let T be an arbitrary n × n matrix with real entries. We explicitly find the closest (in Frobenius norm) matrix A to T , where A is n × n with real entries, subject to the condition that A is “generalized doubly stochastic” (i.e. Ae = e and eA = e , where e = (1, 1, ..., 1) , although A is not necessarily nonnegative) and A has the same first moment as T (i.e. eT1 Ae1 = e T 1 Te1). We also expl...

in this paper, we intend to solve special kind of ordinary differential equations which is called heun equations, by converting to a corresponding stochastic differential equation(s.d.e.). so, we construct a stochastic linear equation system from this equation which its solution is based on computing fundamental matrix of this system and then, this s.d.e. is solved by numerically methods. mo...

In recent years, there has been greater attempt to find numerical solutions of differential equations using wavelet's methods. The following method is based on vector forms of Haar-wavelet functions. In this paper, we will introduce one dimensional Haar-wavelet functions and the Haar-wavelet operational matrices of the fractional order integration. Also the Haar-wavelet operational matrices of ...

In this paper we present a stochastic extension of finite PBC, sPBC, in which actions have a stochastic delay associated, which is taken from a negative exponential distribution. We define for the language both an operational and a denotational semantics, using a class of labelled stochastic Petri net as supporting values. In this paper we restrict our attention to finite sPBC, i.e., we conside...

Graph transformation systems (GTS) have been proposed for high-level stochastic modelling of dynamic systems and networks. The resulting systems can be described as semi-Markov processes with graphs as states and transformations as transitions. The operational semantics of such processes can be explored through stochastic simulation. In this paper, we develop the basic theory of stochastic grap...

The Petri Box Calculus (PBC) combines two well known paradigms of the design of concurrent systems: process algebras and Petri nets. In our first proposal of sPBC (stochastic PBC) [12] we defined a Markovian extension of finite PBC, i.e., we had a Markovian process algebra for which both an operational and a denotational (based on stochastic Petri nets) semantics were defined. Our goal in this ...