Hybrid differential transform-finite difference solution of 2D transient nonlinear annular fin equation

Hybrid differential transform - finite difference solution of 2 D transient nonlinear annular fin equation

One of the primary ways to enhance heat transfer rate is to use extended surfaces or fins. The heat transfer mechanism of fin is to conduct heat from the heat source to fin surface by its thermal conduction, and then dissipates it to surrounding medium by convection. Most common application areas of fins are in combustion engines, heat exchangers and cooling of electronic equipments. Early stud...

A Nonlinear Differential-difference Equation of Growth.

Generalized differential transform method to differential-difference equation

Article history: Received 22 May 2009 Received in revised form 13 September 2009 Accepted 15 September 2009 Available online 19 September 2009 Communicated by A.R. Bishop PACS: 02.30.Jr 02.60.Cb 02.60.Lj

The Numerical Solution of Klein-Gorden Equation by Using Nonstandard Finite Difference

‎In this paper we propose a numerical scheme to solve the one dimensional nonlinear Klein-Gorden equation‎. ‎We describe the mathematical formulation procedure in details‎. ‎The scheme is three level explicit and based on nonstandard finite difference‎. ‎It has nonlinear denominator function of the step sizes‎. ‎Stability analysis of the method has been given and we prove that the proposed meth...

On the Closed-Form Solution of a Nonlinear Difference Equation and Another Proof to Sroysang’s Conjecture

The purpose of this paper is twofold. First we derive theoretically, using appropriate transformation on x(n), the closed-form solution of the nonlinear difference equation x(n+1) = 1/(±1 + x(n)), n ∈ N_0. The form of solution of this equation, however, was first obtained in [10] but through induction principle. Then, with the solution of the above equation at hand, we prove a case ...

NON-STANDARD FINITE DIFFERENCE METHOD FOR NUMERICAL SOLUTION OF SECOND ORDER LINEAR FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS

In this article we have considered a non-standard finite difference method for the solution of second order  Fredholm integro differential equation type initial value problems. The non-standard finite difference method and the composite trapezoidal quadrature method is used to transform the Fredholm integro-differential equation into a system of equations. We have also developed a numerical met...