Shishen Xie

An algorithm for solving bond pricing problem

The nonlinear bond pricing problem has been extensively studied in the literature. Since an analytical solution is not readily available, we will seek to find an approximate solution. We will present a decomposition method, due to Adomian, and show how to obtain a reasonable numerical solution to the bond pricing problem.

On the numerical verification of the asymptotic expansion of Duffing's equation

In this paper a numerical method is implemented for the verification of the order of the asymptotic expansion of Duffings equation. The technique is illustrated by considering the perturbation solution of the equation at some particular values.

Decomposition method for solving a nonlinear business cycle model

In this paper we present a Kaleckian-type model of a business cycle based on a nonlinear delay differential equation. A numerical algorithm based on a decomposition scheme is implemented for the approximate solution of the model. The numerical results of the underlying equation show that the business cycle is stable.

The Asymptotic Expansion and Numerical Verification of Van der Pol's Equation

A technique is presented in this paper to verify the order of accuracy of asymptotic expansion of Van der Pols equation. The technique is focused on using numerical solutions as an independent means of verifying the validity of asymptotic expansions.

Pexider functional equations-their fuzzy analogs

In this paper we shall interpret and study the Pexider functional equations in the context of Fuzzy Set Theory. In particular, we shall present a general procedure for obtaining the fuzzy analog of the Pexider functional equations and then solve the resulting equations.

Numerical approximation for integral equations

A numerical algorithm, based on a decomposition technique, is presented for solving a class of nonlinear integral equations. The scheme is shown to be highly accurate, and only few terms are required to obtain accurate computable solutions.

On a Distributional Analog of a Sum Form Functional Equation

In this paper, we consider a sum form functional equation f(xy) + f(x(1-y)) + f(y(1-x)) + f((1-x)(1-y)) = 0 which arises in characterizing information measures. We will cast it in distributions; and show that for regular distribution we obtain the classical solution.

Numerical Techniques for Solving a Biharmonic Equation in a Sectorial Region

The behavior of fluid in a cavity when subjected to movement of one of its surrounding walls is modeled by a version of the Navier-Stokes equations. The problem to be discussed in this paper can be described as follows: A two-dimensional sectorial cavity

The continuous associated legendre transform

G = \left\{ {\left( {r,\theta } \right)|1 < a, - \alpha < \theta < \alpha } \right\}