The goal of this paper is to calculate of order reduction of the KdV typeequation and the non-isospectral KdV type equation using the μ-symmetrymethod. Moreover we obtain μ-conservation law of the non-isospectral KdVtype equation using the variational problem method.

The paper presents the application of Least Squares moment matching method about a general point „a‟ for the reduction of high order Interval systems. A heuristic criteria have been employed for selecting the linear shift point „a‟ based upon the harmonic mean of real parts of the poles of four high order fixed systems obtained by Kharitonov‟s Theorem. The denominator polynomials are obtained b...

Adaptive wavelet-collocation numerical methods (AWCM) for solving the Euler equations for compressible flow with shock discontinuities are described. An algorithm is constructed to add a minimal but sufficient amount of viscosity in the vicinity of steep gradients, based on the behavior of wavelet coefficients there. This selective addition of numerical viscosity minimizes oscillations in the v...

in this paper, we use a third degree b-spline function to construct an approximate solution forthird order linear and nonlinear boundary value problems coupled with the least square method. severalexamples are given to illustrate the efficiency of the proposed technique.

In this paper, we propose a new approach to nonstandard analysis without using the ultrafilters. This method is very simple in practice. Moreover, we construct explicitly the total order relation in the new field of the infinitesimal numbers. To illustrate the importance of this work, we suggest comparing  a few applications of this approach with the former methods.

conclusions the present research demonstrated that the ultrasonic (us) process can be utilized as an effective and simple method for treatment of mg dye in an aqueous solution. moreover, the eeo is directly proportional to the mg concentration and power density and inversely proportional to temperature and mechanical agitation, which can be predicted by the obtained empirical kinetics model. co...

in this paper, differential transform method (dtm) is described and is applied to solve systems of nonlinear ordinary differential equations which is arising in hiv infections of cell. intervals of validity of the solution will be extended by using pade approximation. the results also will be compared with those results obtained by runge-kutta method. the technique is described and is illustrat...

analysis of the stresses, displacements, and horizontal strains of the ground subsidence due to underground excavation in rocks can be accomplished by means of a hybridized higher order indirect boundary element/finite difference (be/fd) formulation. a semi-infinite displacement discontinuity field is discretized (numerically) using the cubic displacement discontinuity elements (i.e. each highe...

Systems of functional-diierential and functional equations occur in many biological, control and physics problems. They also include functional diierential equations of neutral type as special cases. In this paper we present a numerical method that is based on the continuous extension of the Runge{Kutta method (for ordinary diierential equations) and the collocation method (for functional equat...