Galip Oturanc

Murat Gubes, Galip Oturanc

In this paper, we present the new approximate solutions of famous coupled Ramani Equation. In order to obtain the solution, we use the semi-analytic methods differential transform method (DTM) and reduced form of DTM called reduced differential transform method (RDTM). We compare our proposed methods with exact solution and also compare with together. Numerical results show clearly that DTM and RDTM are very effective and also provide very accurate solutions. Additionally, it should be noted that RDTM is applied very easily, fast and more convergent than DTM for these kind of problems.

Murat Gubes, H. Alpaslan Peker, Galip Oturanc

We consider two nonlinear El Nino Southern Oscillation (ENSO) model to obtain approximate solutions with differential transform method for the first time. Efficiency, accuracy and error rates of solutions are compared with analytic solution, variational iteration and adomian decomposition solutions on the given tables and figures.

Haldun Alpaslan Peker, Galip Oturanc

The aim of this study is to present a reliable combination of the differential transformation method (DTM) and Padé approximants to make, for the first time, a semi-analytic analysis of the problem of free convection boundary-layer flow over a vertical plate as produced by a body force about a flat plate in the direction of the generating body force. Boundary conditions in an unbounded domain, i.e. boundary condition at infinity, pose a problem in general for the numerical solution methods. Without using Padé approximation, the semi-analytical solution obtained by the DTM cannot satisfy infinity boundary conditions. The obtained results are in good agreement with those provided previously by the iterative numerical method. As a result, without taking or estimating missing boundary conditions, the DTM-Padé method provides a simple, non-iterative and effective way for determining the solutions of nonlinear free convection boundary layer problems possessing the boundary conditions at infinity.

Murat Gubes, Yildiray Keskin, Galip Oturanc

This paper is presented to give numerical solutions of some cases of nonlinear wave-like equations with variable coefficients by using Reduced Differential Transform Method (RDTM). RDTM can be applied most of the physical, engineering, biological and etc. models as an alternative to obtain reliable and fastest converge, efficient approximations. Hence, our obtained results showed that RDTM is a very simple method and has a quite accuracy.