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.

We propose solving the inverse eigenvalue problem for symmetric nonnegative matrices by means of a di erential equation. If the given spectrum is feasible, then a symmetric nonnegative matrix can be constructed simply by following the solution curve of the di erential system. The choice of the vector eld is based on the idea of minimizing the distance between the cone of symmetric nonnegative m...

Quantitative analysis of dynamical processes requires a precise estimation of the optical ow eld from image sequences. Most articles evaluating the performance of optical ow techniques focus on the initial formulation of the minimization problem to solve the ill posed brightness change constraint equation. Performance di erences are attributed to slight di erences in the formulation of the mini...

We formulate and study a one-dimensional single-species di¬usive-delay population model. The time delay is the time taken from birth to maturity. Without di¬usion, the delay di¬erential model extends the well-known logistic di¬erential equation by allowing delayed constant birth processes and instantaneous quadratically regulated death processes. This delayed model is known to have simple globa...

| In this short note we present an observability criterion for systems whose state is governed by a matrix Riccati di erential equation and whose output is given by an a ne transformation.

The following backward stochastic Riccati di erential equation (BSRDE in short) 8>>>>><>>>>>>>>>>>: dK = [AK +KA+ d X i=1 C 0 iKCi +Q+ d X i=1 (C 0 iLi + LiCi)

For xed = (x; t), we consider the solution u(f) to u (x; t) + Au(x; t) = f(x) (x; t); x 2 ; t > 0 u(x; 0) = u(x; 0) = 0; x 2 ; Bju(x; t) = 0; x 2 @ ; t > 0; 1 j m; where u = @u @t , u = @ u @t , R, r 1 is a bounded domain with smooth boundary, A is a uniformly symmetric elliptic di erential operator of order 2m with t-independent smooth coe cients, Bj , 1 j m, are t-independent boundary di eren...

Our goal in this paper is to use combined Laplace transform (CLT) and Adomian decomposition method(ADM) (that will be explained section 3), study approximate solutions for non-linear time-fractionalBurger's equation, fractional Burger's Kdv equation the modi?ed theCaputo Conformable derivatives. Comparison between two exact solution made.Here we report that method (LTDM) proved e?cient beused o...

Degenerate parabolic equations of Kolmogorov type occur in many areas of analysis and applied mathematics. In their simplest form these equations were introduced by Kolmogorov in 1934 to describe the probability density of the positions and velocities of particles but the equations are also used as prototypes for evolution equations arising in the kinetic theory of gases. More recently equation...

— We present necessary and su‰cient conditions to guarantee that at least one solution of an infinite dimensional stochastic di¤erential equation, which starts from a regular closed subset K of an Hilbert space, remains in K for all times.