We describe some new algorithm and heuristics for computing the polynomial and rational solutions of bounded degree of a class of ordinary di erential equations, which includes generalized Riccati equations. As a consequence, our methods can be used for factoring linear ordinary di erential equations. Since they generate systems of algebraic equations in at most n unknowns, where n is the order...

in this article, a mathematical model describing the growth orterminating myelogenous leukemia blood cancer's cells against naive t-celland eective t-cell population of body, presented by fractional dierentialequations. we use this model to analyze the stability of the dynamics, whichoccur in the local interaction of eector-immune cell and tumor cells. wewill also investigate the optima...

in this study, a new and ecient approach is presented for numerical solution offredholm integro-dierential equations (fides) of the second kind on unbounded domainwith degenerate kernel based on operational matrices with respect to generalized laguerrepolynomials(glps). properties of these polynomials and operational matrices of integration,dierentiation are introduced and are ultilized to r...

In a di erential equations course, one typically studies a few classes of problems for which there are closed form solutions, such as ordinary, linear di erential equations with constant coe cients. Most problems of interest in real world simulation problems are much more complex, however, involving domains of two or more dimensions or nonlinear e ects, yielding partial di erential equations or...

this paper describes an approximating solution, based on lagrange interpolation and spline functions, to treat functional integral equations of fredholm type and volterra type. this method can be extended to functional dierential and integro-dierential equations. for showing eciency of the method we give some numerical examples.

In this survey we recall the results obtained in [16] where we gave a representation theorem for the solutions of stochastic di¤erential equations in Hilbert spaces. Using this representation theorem and the deterministic characterizations of exponential stability and uniform observability obtained in [16], [17], we will prove a result of Datko type concerning the exponential dichotomy of stoch...

The problem of nding adapted solutions to systems of coupled linear forward-backward stochastic dierential equations (FBSDEs, for short) is investigated. A necessary condition of solvability leads to a reduction of general linear FBSDEs to a special one. By some ideas from controllability in control theory, using some functional analysis, we obtain a necessary and sucient condition for the solv...

| Four schemes for linearizing the transconductance of the basic di erential pair in subthreshold CMOS are examined. They are: source degeneration via (1) diode-connected transistors, (2) a single di usor and (3) symmetric di usors, and (4) multiple asymmetric di erential pairs. We derive equations for the di erential output current for each linearizing technique. We apply a maximally at optimi...

In this paper, we investigate the almost surely asymptotic stability for the nonlinear stochastic di erential delay equations with Markovian switching. Some su0cient criteria on the controllability and robust stability are also established for linear stochastic di erential delay equations with Markovian switching. ? 2003 Elsevier Ltd. All rights reserved.

In a series of papers, starting with [Fully nonlinear stochastic partial di¤erential equations. C. R. Acad. Sci. Paris Sér. I Math. 326 (1998), no. 9] Lions and Souganidis proposed a (pathwise) theory for fully non-linear stochastic partial di¤erential equations. We present here a (partial) extension towards certain spatial dependence in the noise term. The main novelty is the use of rough path...