pollution has become a very serious threat to our environment. monitoring pollution is the rst step toward planning to save the environment. the use of dierential equations, monitoring pollution has become possible. in this paper, a ritz-collocation method is introduced to solve non-linear oscillatory systems such as modelling the pollution of a system of lakes. the method is based upon bernoul...

a simple new closed form of the green function for axisymmetric magnetostatic problemsis found analytically in cylindrical coordinates. the result is verified by applying several examples.

Introduction Time discretization approximation schemes for solutions of stochastic dierential equations have been studied by many people and are treated, e.g. in the book of Kloeden-Platen [Kl-Pl92]. Since heat kernels are the probability densities of the law of solutions, it might be worthwhile to ask if these approximation schemes provide a natural scheme of approximation for heat kenrnels. P...

In this paper, we study inextensible ows in three dimensional Lie groups with a bi-invariant metric. The necessary and sucient conditions for inextensible curve ow are expressed as a partial dierential equation involving the curvatures. Also, we give some results for special cases of Lie groups.

In this paper, modication 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 modied algorithm give the exact solution for dierential equations by using one iterationonly.

When solving a partial dierential equation on a MIMD distributed memory computer there arises the problem of distributing the mesh so that the communication requirement of the numerical solver is minimised subject to a load balancing constraint. In this paper we introduce a new algorithm for this partitioning problem for unstructured meshes and study its properties, along with those of other co...

Random invariant manifolds are geometric objects useful for understanding complex dynamics under stochastic influences. Under a nonuniform hyperbolicity or a nonuniform exponential dichotomy condition, the existence of random pseudostable and pseudo-unstable manifolds for a class of random partial differential equations and stochastic partial differential equations is shown. Unlike the invarian...

in this paper, a high-order and conditionally stable stochastic difference scheme is proposed for the numerical solution of $rm ithat{o}$ stochastic advection diffusion equation with one dimensional white noise process. we applied a finite difference approximation of fourth-order for discretizing space spatial derivative of this equation. the main properties of deterministic difference schemes,...

Nonlinear Diff. Eqns. Appl. (NoDEA) 10(2003), 431-454. Determining functionals are tools to describe the finite dimensional longterm dynamics of infinite dimensional dynamical systems. There also exist several applications to infinite dimensional random dynamical systems. In these applications the convergence condition of the trajectories of an infinite dimensional random dynamical system with ...