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...

Introduction In this paper we consider cell centered nite di erence approximations for second order convection di usion equations of divergence type Our goal is to construct nite di erence methods of second order of approximation that satisfy the discrete maximum principle The error estimates are in the discrete Sobolev spaces associated with the considered boundary value problem Approximation ...

The equivalence of the discretized equations resulting from both uctuation splitting and nite volume schemes is demonstrated in one dimension. Scalar equations are considered for advection, di usion, and combined advection/diffusion. Analysis of systems is performed for the Euler and Navier-Stokes equations of gas dynamics. Non-uniform mesh-point distributions are included in the analyses.

In earlier work we constructed a class of spherically symmetric, ̄uid dynamical shock waves that satisfy the Einstein equations of general relativity. These shock waves extend the celebrated Oppenheimer-Snyder result to the case of non-zero pressure. Our shock waves are determined by a system of ordinary di€erential equations that describe the matching of a FriedmannRobertson-Walker metric (a c...

An explicit nite element method is used to solve the linear convection di usion reaction equations governing contaminant transport in ground water owing through an adsorbing porous medium The use of discontinuous nite elements for the convective part of the equations combined with mixed nite elements for the di usive part renders the method for the concentration solution which displays strong g...

Paradigm-based approaches to word processing/learning assume that word forms are not acquired in isolation, but through associative relations linking members of the same word family (e.g. a paradigm, or a set of forms filling the same paradigm cell). Principles of correlative learning offer a set of dynamic equations that are key to modelling this complex dynamic at a considerable level of deta...

The focus of this paper is on the numerical solution of large sparse non-linear systems of algebraic 9 equations on parallel computers. Such non-linear systems often arise from the discretization of non-linear partial di erential equations, such as the Navier–Stokes equations for uid ows, using nite element 11 or nite di erence methods. A traditional inexact Newton method, applied directly to t...

We investigate the derivation and the mathematical properties of a Saint-Venant model with an energy equation and with temperature-dependent transport coe±cients. These equations model shallow water °ows as well as thin viscous sheets over °uid substrates like oil slicks, atlantic waters in the Strait of Gilbraltar or °oat glasses. We exhibit an entropy function for the system of partial di®ere...

In this paper, we are concerned with oscillation of the nonlinear di¤erence equation (cn [ (dn xn)] ) + qnf(xg(n)) = 0; n n0; where > 0 is the quotient of odd positive integers, cn, dn and qn are positive sequences of real numbers, g(n) is a sequence of nonnegative integers and f 2 C(R;R) such that uf(u) > 0 for u 6= 0:We establish some new su¢ cient conditions for oscillation by employing the ...