WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12573/394
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Article Citation - WoS: 28Citation - Scopus: 25An Efficient Approach to Numerical Study of the MRLW Equation With B-Spline Collocation Method(Hindawi Ltd, 2014) Karakoc, Seydi Battal Gazi; Ak, Turgut; Zeybek, Halil; Karakoҫ, Seydi Battal GaziA septic B-spline collocation method is implemented to find the numerical solution of the modified regularized long wave (MRLW) equation. Three test problems including the single soliton and interaction of two and three solitons are studied to validate the proposed method by calculating the error norms L-2 and L-infinity and the invariants I-1, I-2, and I-3. Also, we have studied the Maxwellian initial condition pulse. The numerical results obtained by the method show that the present method is accurate and efficient. Results are compared with some earlier results given in the literature. A linear stability analysis of the method is also investigated.Article Citation - WoS: 24Citation - Scopus: 27A Numerical Investigation of the GRLW Equation Using Lumped Galerkin Approach With Cubic B-Spline(Springer International Publishing AG, 2016-02-27) Zeybek, Halil; Karakoc, S. Battal GaziIn this work, we construct the lumped Galerkin approach based on cubic B-splines to obtain the numerical solution of the generalized regularized long wave equation. Applying the von Neumann approximation, it is shown that the linearized algorithm is unconditionally stable. The presented method is implemented to three test problems including single solitary wave, interaction of two solitary waves and development of an undular bore. To prove the performance of the numerical scheme, the error norms L-2 and L-infinity and the conservative quantities I-1, I-2 and I-3 are computed and the computational data are compared with the earlier works. In addition, the motion of solitary waves is described at different time levels.Article A New Approach for Numerical Solution of Linear and Non-Linear Systems(Korean Soc Computational & Applied Mathematics & Korean Sigcam, 2017) Zeybek, Halil; Dolapci, Ihsan TimucinIn this study, Taylor matrix algorithm is designed for the approximate solution of linear and non-linear differential equation systems. The algorithm is essentially based on the expansion of the functions in differential equation systems to Taylor series and substituting the matrix forms of these expansions into the given equation systems. Using the Mathematica program, the matrix equations are solved and the unknown Taylor coefficients are found approximately. The presented numerical approach is discussed on samples from various linear and non-linear differential equation systems as well as stiff systems. The computational data are then compared with those of some earlier numerical or exact results. As a result, this comparison demonstrates that the proposed method is accurate and reliable.