http://belgelik.isikun.edu.tr/xmlui/handleiubelgelik/2391 JAEM 2012, Vol 2, No 2 koleksiyonunu içerir. Tue, 07 Apr 2026 10:41:48 GMT 2026-04-07T10:41:48Z http://belgelik.isikun.edu.tr/xmlui/handleiubelgelik/6039 Contribution of higher order terms to the nonlinear shallow water waves Demiray, Hilmi In this work, by utilizing the scaled multiple-space expansion method, we studied the propagation of weakly nonlinear waves in shallow water and obtained the governing evolution equations of various order terms in the perturbation expansion. Seeking a progressive wave solution to these evolution equations we obtained the speed correction terms so as to remove some possible secularities. The result obtained here is exactly the same with that of obtained by the modified reductive perturbation method [12]. We also proposed a method for the evolution equation governing the n th order term in the perturbation expansion. By defining a single time parameter we showed the connection of the modified reductive perturbation method to the scaled multiple-space expansion method. Sun, 01 Apr 2012 00:00:00 GMT http://belgelik.isikun.edu.tr/xmlui/handleiubelgelik/6039 2012-04-01T00:00:00Z http://belgelik.isikun.edu.tr/xmlui/handleiubelgelik/2482 Series solution of epidemic model Doğan, Nurettin; Akın, Ömer The present paper is concerned with the approximate analytic series solution of the epidemic model. In place of the traditional numerical, perturbation or asymtotic methods, Laplace-Adomian decomposition method (LADM) is employed.To demonstrate the effort of the LADM an epidemic model, which has been worked on recently, has been solved. The results are compared with the results obtained by Adomian decomposition method and homotopy perturbation method. Furthermore the results are compared with Fouth Order Runge Method and residual error. After examining the results, we see that LADM is a powerful method for obtaining aproximate solutions to epidemic model. Wed, 17 Oct 2012 00:00:00 GMT http://belgelik.isikun.edu.tr/xmlui/handleiubelgelik/2482 2012-10-17T00:00:00Z http://belgelik.isikun.edu.tr/xmlui/handleiubelgelik/2481 Asymptotic expansions for the ergodic moments of a semi-markovian random walk with a generalized delaying barrier Khaniyev, Tahir; Marandi, Ali Akbar Fattahpour; Ünver, İhsan In this study, a semi-Markovian random walk process (X(t)) with a generalized delaying barrier is considered and the ergodic theorem for this process is proved under some weak conditions. Then, the exact expressions and asymptotic expansions for the first four ergodic moments of the process X(t) are obtained. Sun, 01 Jan 2012 00:00:00 GMT http://belgelik.isikun.edu.tr/xmlui/handleiubelgelik/2481 2012-01-01T00:00:00Z http://belgelik.isikun.edu.tr/xmlui/handleiubelgelik/2480 Energy preserving integratıon of KDV-KDV systems Karasözen, Bülent; Şimşek, Görkem Coupled Korteweg de Vries (KdV) equations in Hamiltonian form are integrated by the energy preserving average vector field (AVF) method. Numerical results confirm long term preservation of the energy and the quadratic invariants. Produced generalized solitary waves are similar to those in the literature for larger mesh sizes and time steps. Numerical and continuous dispersion relations of the linearized equations are compared to analyze the behavior of the traveling waves and the interaction of the solitons. Sun, 01 Jul 2012 00:00:00 GMT http://belgelik.isikun.edu.tr/xmlui/handleiubelgelik/2480 2012-07-01T00:00:00Z