one of the ecient and powerful schemes to solve linear and nonlinear equationsis homotopy analysis method (ham). in this work, we obtain the approximate solution ofa system of partial dierential equations (pdes) by means of ham. for this purpose, wedevelop the concept of ham for a system of pdes as a matrix form. then, we prove theconvergence theorem and apply the proposed method to nd the a...

If u(t; x) is a solution of a one{dimensional, parabolic, second{order, linear partial di erential equation (PDE), then it is known that, under suitable conditions, the number of zero{crossings of the function u(t; ) decreases (that is, does not increase) as time t increases. Such theorems have applications to the study of blow{up of solutions of semilinear PDE, time dependent Sturm Liouville t...

Stochastic di erential games are considered in a non-Markovian setting. Typically, in stochastic di erential games the modulating process of the di usion equation describing the state ow is taken to be Markovian. Then Nash equilibria or other types of solution such as Pareto equilibria are constructed using Hamilton-Jacobi-Bellman (HJB) equations. But in a non-Markovian setting the HJB method i...

We present a new method for the solution of partial di erential equations. In contrast to the usual approach which needs in the 2-D case O(h 2 n ) grid points, our combination technique works with only O(h 1 n ld(h 1 n )) grid points, where h n denotes the employed grid size. The accuracy of the obtained solution deteriorates only slightly from O(h 2 n ) to O(h 2 n ld(h 1 n )) for a su ciently ...

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...

Once ReΨ and ImΨ are found from these two coupled di erential equations, the time-dependent probability density |Ψ| for a particle represented by the wave function Ψ can be calculated from |Ψ| = Ψ∗Ψ = (ReΨ) + (ImΨ), where the * denotes the complex conjugate. Our task, then, is to solve Equations (2) and (3) numerically, and this computational approach requires that the partial derivatives be ap...

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...

We study a Hamilton± Jacobi partial di€ erential equation, arising in an optimal control problem for an a ne non-linear singularly perturbed system. This equation is solvable i€ there exists a special invariant manifold of the corresponding Hamiltonian system. We obtain exact slow± fast decomposition of the Hamiltonian system and of the special invariant manifold into slow and fast components....