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...

We investigate the directed random walk on hierarchic trees. Two cases are investigated: random variables on deterministic trees with a continuous branching, and random variables on the trees constructed through the random branching process. We derive renormalization group (partial differential) equations for the branching models with binomial, Poisson, and compound Poisson distributions of ran...

Partial difference equations are difference equations that involve functions with two or more independent integer variables. Such equations arise from considerations of random walk problems, molecular structure problems, and numerical difference approximation problems. Recently, there have been a large number of papers devoted to partial difference equations, and the problem of oscillatory of s...

In this paper we introduce a method for generating unstructured meshes in parallel which are partitioned in a \good" way. When solving a partial dierential equation on a parallel distributed memory machine, the mesh should be decomposed so that the communication requirement of the numerical solver is minimised and also the amount of work to be performed on each processor is approximately equal....

solitons are ubiquitous and exist in almost every area from sky to bottom. for solitons to appear, the relevant equation of motion must be nonlinear. in the present study, we deal with the korteweg-devries (kdv), modied korteweg-de vries (mkdv) and regularised longwave (rlw) equations using homotopy perturbation method (hpm). the algorithm makes use of the hpm to determine the initial expansio...

In this thesis, we study uniform controllability properties of semi-discrete approximations for parabolic systems. In a first part, we address the minimization of the Lq-norm (q > 2) of semidiscrete controls for parabolic equation. As shown in [LT06], under the main approximation assumptions that the discretized semigroup is uniformly analytic and that the degree of unboundedness of control ope...