Browsing by Author "Koroglu, Canan"

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A New Conservative Numerical Method for Strongly Coupled Nonlinear Schrödinger Equations
(Springer Heidelberg, 2025) Ors, Ridvan Fatih; Koroglu, Canan; Aydin, Ayhan
In this paper, a numerical method based on the conservative finite difference scheme is constructed to numerically solve the strongly coupled nonlinear Schr & ouml;dinger (SCNLS) equation. Conservative properties such as energy and mass of the SCNLS equation have been proven. In particular a fourth-order central difference scheme is used to discretize the the spatial derivative and a second-order Crank-Nicolson type discretization is used to discretize the temporal derivative. It has been shown that the proposed scheme preserves the discrete mass and energy. The existence of discrete solution is also investigated. Several numerical results are given to demonstrate the preservation properties of the new method. Also, the effect of the linear coupling parameters on the evolution of solitary waves is investigated.
Citation - WoS: 9
Citation - Scopus: 10
A nonstandard numerical method for the modified KdV equation
(indian Acad Sciences, 2017) Aydin, Ayhan; Koroglu, Canan
A linearly implicit nonstandard finite difference method is presented for the numerical solution of modified Korteweg-de Vries equation. Local truncation error of the scheme is discussed. Numerical examples are presented to test the efficiency and accuracy of the scheme.
Citation - WoS: 4
Citation - Scopus: 5
An Unconventional Finite Difference Scheme for Modified Korteweg-De Vries Equation
(Hindawi Ltd, 2017) Koroglu, Canan; Aydin, Ayhan
A numerical solution of the modified Korteweg-de Vries (MKdV) equation is presented by using a nonstandard finite difference (NSFD) scheme with theta method which includes the implicit Euler and a Crank-Nicolson type discretization. Local truncation error of the NSFD scheme and linear stability analysis are discussed. To test the accuracy and efficiency of the method, some numerical examples are given. The numerical results of NSFD scheme are compared with the exact solution and a standard finite difference scheme. The numerical results illustrate that the NSFD scheme is a robust numerical tool for the numerical integration of the MKdV equation.