Theory of Approximation and Applications
Volume:6 Issue: 1, Winter and Spring 2010

Here, Adomian decomposition method has been used for nding approximateand numerical solutions of nonlinear dierential dierence equations arising inmathematical physics. Two models of special interest in physics, namely, theHybrid nonlinear dierential dierence equation and Relativistic Toda couplednonlinear dierential-dierence equation are chosen to illustrate the validity andthe great potential of the proposed method. Comparisons are made between theresults of the proposed method and exact solutions. The results show that theAdomian Decomposition Method is an attractive method in solving the non-linear dierential dierence equations. It is worthwhile to mention that theAdomian decomposition method is also easy to be applied to other nonlineardierential dierence equation arising in physics.

In this letter, generalized dierential transform (GDTM) method is used tosolve nonlinear dierential dierence equation for the rst time. Two models ofspecial interest in mathematical physics are chosen to illustrate the validity andthe great potential of the generalized dierential transform method.Comparisons are made between the results of the proposed method and exactsolutions. Applying the proposed method for two models, namely, Lotka-Volteranonlinear dierence equation and Relativistic Toda lattice dierence equations,and successfully obtain solitary wave solutions.We should point out that generalized dierential transform method is also easyto be applied to other nonlinear dierential dierence equation arising in physics.

In this paper we propose a simple non-parametric model for multiple criteriasupplier selection problem. The proposed model does not generate a zero weightfor a certain criterion and ranks the suppliers without solving the model n times(one linear programming (LP) for each supplier) and therefore allows the man-ager to get faster results. The methodology is illustrated using an example.

In this paper, we introduce a new xed point theorem in cone metric spacesand given an application of this theorem to prove the existence and unicity ofsolution for a new integral equation.

This paper presents a method of solving Abel integral equation by usingChebyshev wavelets. In the proposed method, the functions in Abel integralequation are approximated based on Chebyshev wavelet and therefore, the solv-ing of Abel integral equation is reduced to the solving of linear algebraic equa-tions. This presented method are demonstrated and validated through severalnumerical examples.

Let p(z) = Pn j=0 ajzj be a polynomial of degree n and letM(p; r) = maxjzj=r jp(z)j:In this paper we prove some sharp inequalities concerning the coecients of thepolynomial p(z) with restricted zeros. We also establish a sucient conditionfor the separation of zeros of p(z):

this paper we formulate and prove some xed and common xed pointTheorems for self-mappings dened on complete lower Transversal functionalprobabilistic spaces.

In discussing continuation in two-dimensional elasticity it is necessary to usecertain results concerning the boundary values of Cauchy's integrals [1], [2]. Thepurpose of this paper is to introduce the value of Cauchy's integral at a point onthe line and then consider the limiting value of Cauchy's integral as z approachest0 from points not on line.

In this work Haar wavelet approach is used for solving Volterra and Fredholmintegro dierential equations. For this purpose the main problem is reduced toa system of linear algebraic equations. An detailed error analysis is worked outand four test problems for which the exact solution is known are considered.

In this article, we construct the exact traveling wave solutions for couplednonlinear evolution equations in mathematical physics via the Hirota-Satsumacoupled KdV equations, the Konopelchenko- Dubrovsky coupled equations andthe Drinfeld- Sokolov- Wilson coupled equations by using a generalized (GG)􀀀 ex- pansion method. The main idea of this alternative approach is that the travelingwave solutions of nonlinear dierential equations can be expressed by a poly-nomial in (G G); where G = G() satises the nonlinear rst order dierentialequation. As a result, some new travelling wave solutions involving parame-ters, expressed by dierent Jacobi elliptic functions are obtained. The proposedmethod is straightforward, concise, eective and can be applied to other non-linear evolution equations in mathematical physics.