in this paper a numerical method for solving forth order fuzzy dierentialequations under generalized differentiability is proposed. this method is basedon the interpolating a solution by piecewise polynomial of degree 8 in the rangeof solution . we investigate the existence and uniqueness of solutions. finally anumerical example is presented to illustrate the accuracy of the new technique.

In this paper we present an approach for the numerical solution of Delay Di erential Equations y 0 (t) = Ly (t) +My (t ) t 0 y (t) = ' (t) t 0; (1) where > 0, L;M 2 C I m m and ' 2 C ([ ; 0] ; C I m ), di erent from the classical step-by-step method. We restate (1) as an abstract Cauchy problem and then we discretize it in a system of Ordinary Differential Equations. The scheme of discretizatio...

We derive a rst-order approximation of the density of maximum entropy for a continuous 1-D random variable, given a number of simple constraints. This results in a density expansion which is somewhat similar to the classical polynomial density expansions by Gram-Charlier and Edgeworth. Using this approximation of density, an approximation of 1-D diierential entropy is derived. The approximation...

We consider polynomials in two variables which satisfy an admissible second order partial differential equation of the form (*) Auxx + 2Buxy + Cuyy +Dux + Euy = u; and are orthogonal relative to a symmetric bilinear form de…ned by '(p; q) = h ; pqi+ h ; pxqxi ; where A; ; E are polynomials in x and y; is an eigenvalue parameter, and are linear functionals on polynomials. We …nd a condition for ...

We investigate numerical valuation of cross-currency interest rate-based derivatives under Babbs' extended Vasicek-style model by numerical solution of the associated partial di erential equation (PDE) | in particular, we consider the terminable di erential (di ) swap. Firstly we precisely formulate, in terms of their cash ows, various types of single and cross-currency swaps and swaptions. We ...

The Poisson-Boltzmann (PB) equation describes the electrostatic potential of a biomolecular system composed by a molecule in a solvent. The electrostatic potential is involved in biomolecular models which are used in molecular simulation. In consequence, nding an e cient method to simulate the numerical solution of PB equation is very useful. As a rst step, we establish in this paper a probabil...

Deterministic di€erential equation models indicate that partnership concurrency and non-homogeneous mixing patterns play an important role in the spread of sexually transmitted infections. Stochastic discreteindividual simulation studies arrive at similar conclusions, but from a very di€erent modeling perspective. This paper presents a stochastic discrete-individual infection model that helps t...

In the talk we present a survey of the current state of art in the area of quadratic functionals with prescribed time derivatives. The …rst contribution dedicated to the topic was that by Yu.M. Repin [5]. In this seminal contribution a quadratic functional of a general form was suggested. The time derivative of the functional has been computed, and then, equating the derivative to the prescribe...

This article shows how a (linear) scale-space representation can be de ned for discrete signals of arbitrary dimension. The treatment is based upon the assumptions that (i) the scale-space representation should be de ned by convolving the original signal with a one-parameter family of symmetric smoothing kernels possessing a semi-group property, and (ii) local extrema must not be enhanced when ...

in this paper, we prove the existence of the solution for boundary value prob-lem(bvp) of fractional dierential equations of order q 2 (2; 3]. the kras-noselskii's xed point theorem is applied to establish the results. in addition,we give an detailed example to demonstrate the main result.