in this work, we conduct a comparative study among the combine laplace transform and modied adomian decomposition method (lmadm) and two traditional methods for an analytic and approximate treatment of special type of nonlinear volterra integro-differential equations of the second kind. the nonlinear part of integro-differential is approximated by adomian polynomials, and the equation is red...

The main topics of this technical report are quaternions, their mathematical properties, and how they can be used to rotate objects. We introduce quaternion mathematics and discuss why quaternions are a better choice for implementing rotation than the well-known matrix implementations. We then treat di erent methods for interpolation between series of rotations. During this treatment we give co...

In this paper we describe an experimental system called d dt for approximating reachable states for hybrid systems whose con tinuous dynamics is de ned by linear di erential equations We use an approximation algorithm whose accumulation of errors during the con tinuous evolution is much smaller than in previously used methods The d dt system can so far treat non trivial continuous systems hybri...

The analytic expression of the time evolution of the Reynolds stress anisotropy tensor in all planar homogeneous ows is obtained by exact integration of the modeled di erential Reynolds stress equations. The procedure is based on results of tensor representation theory, is applicable for general pressure-strain correlation tensors, and can account for any additional turbulence anisotropy e ects...

Stability of stochastic di#erential equations with Markovian switching has recently been discussed by many authors, for example, Basak et al. (J. Math. Anal. Appl. 202 (1996) 604), Ji and Chizeck (IEEE Trans. Automat. Control 35 (1990) 777), Mariton (Jump Linear System in Automatic Control, Marcel Dekker, New York), Mao (Stochastic Process. Appl. 79 (1999) 45), Mao et al. (Bernoulli 6 (2000) 73...

The discontinuous Galerkin (dG) method for time integration of the parabolic problem obtained when pricing options using the BlackScholes partial di↵erential equation is presented. By decoupling of the large system of equations needed to be solved in each time step, the time of computation and memory requirement is significantly reduced. Even though there is a discontinuity in the first derivat...

We present a Petri net formalism that allows for mixed discrete and continuous stochastic models. The continuous part of the models consists of uid places that are lled and emptied at random (normally distributed) rate. Fluid places can be used for the modelling of continuous system components as well as for continuous approximation of heavily loaded discrete places in order to avoid state spac...

An axiomatic concept of quantum eld theory stochastic processes is introduced and some elementary properties of them are presented. The existence of the trace processes connected to Gibbs random elds obtained in Euclidean Quantum Field Theory is discussed. For particular twodimensional interactions the Markov property and continuity of paths of the corresponding trace processes have been obtain...

Let X be the solution of an Itô di erential equation with jumps over R. Under some auxiliary assumptions on the parameters of the equation, we characterize the support of the law of X in the Skorohod space D as the closure of the set of solutions to piecewise ordinary di erential equations. This gives an analogue in the Poisson space to the classical Stroock–Varadhan support theorem. c © 2000 P...

in this paper, modication of the optimal homotopy asymptotic method (moham) is appliedupon singular initial value lane-emden type equations and results are compared with the available exactsolutions. the modied algorithm give the exact solution for dierential equations by using one iterationonly.