Ahmet Gökdoğan

Adaptive multi-step differential transformation method to solving nonlinear differential equations

Abstract In this paper, we propose a fast and effective adaptive algorithm for the multi-step differential transformation method (MsDTM). This approach named as the adaptive MsDTM is applied to a number of nonlinear differential equations and numerical results are given. At the same time, a comparison between the MsDTM and the adaptive MsDTM reveals that the proposed approach is an efficiency tool for solving the considered equations using fewer time steps.

Numerical Simulation of Fractional Fornberg-Whitham Equation by Differential Transformation Method

An approximate analytical solution of fractional Fornberg-Whitham equation was obtained with the help of the two-dimensional differential transformation method (DTM). It is indicated that the solutions obtained by the two-dimensional DTM are reliable and present an effective method for strongly nonlinear partial equations. Exact solutions can also be obtained from the known forms of the series solutions.

Numerical solution of time‐fraction modified equal width wave equation

Purpose – The purpose of this paper is to show how an application of fractional two dimensional differential transformation method (DTM) obtained approximate analytical solution of time‐fraction modified equal width wave (MEW) equation.Design/methodology/approach – The fractional derivative is described in the Caputo sense.Findings – It is indicated that the solutions obtained by the two dimensional DTM are reliable and that this is an effective method for strongly nonlinear partial equations.Originality/value – The paper shows that exact solutions can also be obtained from the known forms of the series solutions.

Solution of time‐fractional generalized Hirota‐Satsuma coupled KdV equation by generalised differential transformation method

Purpose – In this article, the aim is to obtain an approximate analytical solution of time‐fraction generalized Hirota‐Satsuma coupled KDV with the help of the two dimensional differential transformation method (DTM). Exact solutions can also be obtained from the known forms of the series solutions.Design/methodology/approach – Two dimensional differential transformation method (DTM) is used.Findings – In this paper, the fractional differential transformation method is implemented to the solution of time‐fraction generalized generalized Hirota‐Satsuma coupled KDV with a number of initial and boundary values has been proved. DTM can be applied to many complicated linear and strongly nonlinear partial differential equations and does not require linearization, discretization, restrictive assumptions or perturbation. The presented method is a numerical method based on the generalised Taylor series expansion which constructs an analytical solution in the form of a polynomial.Originality/value – This is an orig...

A new approach stereo based palmprint extraction in unrestricted postures

Regarding the palms recognition system studies, despite achieving a high success rate, hygiene problems in systems with contact and problems arising from changes in the alignment of the hand pose in non-contact ones have been encountered. To resolve these problems, 3D palmprint recognition systems have been developed, however these systems have not had the opportunity to spread due to expensive technologies used as well as low screening rates. In this study, to calculate the position and orientation of a palm in 3D space, a stereo camera system is proposed, with the help of these values by adjusting the geometric image of the palm is converted to a 2D environment. From these images, patterns used for recognition are extracted by using Active Appearance Models. Thus a non-contact system has been achieved, but also patterns that can be used by powerful 2D recognition systems have also been produced.

A Multistage Variational Iteration Method for Solution of Delay Differential Equations

Abstract In this paper, the approximate solution of delay differential equations is obtained by a reliable algorithm based on an adaptation of the classical variational iteration method (VIM), which is called the multi-stage variational iteration method (MSVIM). Examples are carried out and numerical results with comparison to exact solutions, VIM and MATLAB dde23 solver are given. The comparison reveals that the MSVIM is a promising tool to solve delay differential equations.

Numerical Approximations to Solution of Biochemical Reaction Model

In this paper, approximate analytical solution of biochemical reaction model is used by the multi-step differential transform method (MsDTM) based on classical differential transformation method (DTM). Numerical results are compared to those obtained by the fourth-order Runge-Kutta method to illustrate the preciseness and effectiveness of the proposed method. Results are given explicit and graphical form.

Comparative Analysis of Free Optical Vibration of Lamination Composite Optical Beams Using the Boubaker Polynomials Expansion Scheme and the Differential Quadrature Method

The effects of stacking sequences of composite laminated optical beams on free vibration frequencies are investigated using two methods: the Boubaker Polynomials Expansion Scheme (pbes) and the Differential Quadrature Method (dqm). In the last decades, these two techniques have been separately performed for obtaining accurate numerical solutions to several initial boundary value problems (Vo et al. 2010, Li et al. 2008, Chen 2003, Hu et al. 2008, Karami et al. 2003, Malekzadeh et al. 2004, Khare et al. 2004, Della and Shu 2005, Ramtekkar et al. 2002, Adam 2003). Conjointly yielded results are compared and discussed.

Numerical Approximations to the Solution of Ray Tracing through the Crystalline Lens

An approximate analytical solution in the form of a rapidly convergent series for tracing light rays through an inhomogeneous graded index medium is developed, using the multi-step differential transform method based on the classical differential transformation method. Numerical results are compared to those obtained by the fourth-order Runge—Kutta method to illustrate the precision and effectiveness of the proposed method. Results are given in explicit and graphical forms.