Alper Korkmaz

Bio: Alper Korkmaz is an academic researcher from Weimar Institute. The author has contributed to research in topics: Boundary value problem & Nonlinear system. The author has an hindex of 27, co-authored 79 publications receiving 1777 citations. Previous affiliations of Alper Korkmaz include Eskişehir Osmangazi University & Çankırı Karatekin University.

Shock wave simulations using Sinc Differential Quadrature Method

Abstract: Purpose – This paper aims to present a numerical solution of non‐linear Burger's equation using differential quadrature method based on sinc functions.Design/methodology/approach – Sinc Differential Quadrature Method is used for space discretization and four stage Runge‐Kutta algorithm is used for time discretization. A rate of convergency analysis is also performed for shock‐like solution. Numerical stability analysis is performed.Findings – Sinc Differential Quadrature Method generates more accurate solutions of Burgers' equation when compared with the other methods.Originality/value – This combination, Sinc Differential Quadrature and Runge‐Kutta of order four, has not been used to obtain numerical solutions of Burgers' equation.

Traveling wave solution of conformable fractional generalized reaction Duffing model by generalized projective Riccati equation method

Abstract: The generalized projective Riccati equation method is proposed to establish exact solutions for generalized form of the reaction Duffing model in fractional sense namely, Khalil’s derivative. The compatible traveling wave transform converts the governing equation to a non linear ODE. The predicted solution is a series of two new variables that solve a particular ODE system. Coefficients of terms in the series are calculated by solving an algebraic system that comes into existence by substitution of the predicted solution into the ODE which is the result of the wave transformation of the governing equation. Returning original variables give exact solutions to the governing equation in various forms.

A large family of optical solutions to Kundu–Eckhaus model by a new auxiliary equation method

Abstract: The present study suggests a large family of optical solutions to the Kundu–Eckhaus model. Modified form of an auxiliary equation approach have been used to set the solution families. Compatible variable transform reduces the governing equation to a non linear ordinary differential equation. The parameters of the predicted solution in finite series form are determined by substitution of the solution into this ODE. The results cover a large family of optical solutions that are determined by implementation of various techniques in the literature. In this perspective, the modifed form of the a auxiliary equation approach is evaluated as a generalization of different methods widely used to construct the solutions.

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

Abstract: to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.