Elias Deeba

Analysis by fuzzy difference equations of a model of CO2 level in the blood

In this paper we shall consider a model to determine the carbon dioxide (CO2) level in the blood. The model consists of a set of nonlinear difference equations. However, the linearized model will be solved. Since many measurements and factors that determine the CO2 level in the blood may be imprecise, we will consider the fuzzy analog of the linearized model as a method to compensate for these imprecise measurements. We will estimate, for a fixed threshold α, a solution to the fuzzy difference equation with belief at least α. We will show that the results reduce to the classical case when the fuzzy quantities are replaced by crisp ones.

A fuzzy difference equation with an application

Difference equations arise in the modeling of many interesting problems. “Measurements” of data or specified information for an underlying problem may be imprecise or only partially specified. This motivates us to initiate a study of “fuzzy difference equations.” In this paper, we will formulate and solve a given difference equation in the fuzzy setting and give a general method for dealing with any first order difference equation.

The decomposition method applied to Chandrasekhar H-equation

In this paper, Adomians decomposition method is applied to the nonlinear Chandrasekhar H-equation. The solution is expressed as an infinite series. It is shown that two or three iterations are sufficient to obtain good approximation of the exact solution. Adomians method has been illustrated by considering some particular cases of this nonlinear integral equation that are of physical interest.

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.

Distributional analog of a functional equation

Abstract In this paper, we shall apply an operator method for casting and solving the distributional analog of functional equations. In particular, the method will be employed to solve f 1 ( x + y ) + f 2 ( x - y ) + f 3 ( xy ) = 0

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.

The solution of a two-compartment model

Abstract In this paper, a decomposition method is used for solving a two-compartment model incorporating nonlinear efflux from a peripheral compartment. The solution is useful for estimating the parameters and solving the structural identifiability of the model. The technique is demonstrated by considering two different forms of nonlinear transfer efflux.

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.

Bernoulli numbers and trigonometric functions

In this survey article we develop some properties of the Bernoulli numbers and exhibit series expansions, for trigonometric and hyperbolic functions, whose coefficients are given in terms of these numbers. In particular, we present series expansion for the tangent, cotangent, cosecant and hyperbolic cotangent functions. As a consequence of these representations we obtain a formula for the sum of the series ?k 8= i(1/k2n ) for n = 1, 2 . . . . Hopefully the material of this paper will be useful in the teaching of many undergraduate courses.