Lineer Olmayan Birinci Mertebeden Differential Denklem Sistemlerinin Kuvvet Serisiyle Çözümü

DergiPark: 245859trakyafbdBu makalede, lineer olmayan adi diferansiyel denklemlerin çözümü için kuvvet serisini kullandık. Nümerik yoldan elde edilen sonuçlarla, teorik yoldan elde edilen sonuçlar karşılaştırıldı ve lineer olmayan differansiyel denklem sistemlerinde metodun etkinliğini göstermek için örnekler verildi. Nümerik hesap-lamalarda MAPLE bilgisayar cebiri sistemleri kullanıldı (FRANK, 1996).In this paper, we use power series method to solve non-linear ordinary differential equations Theoretical considerations has been discussed and some examples were presented to show the ability of the method for non-linear systems of differential equations. We use MAPLE computer algebra systems for numerical calculations (FRANK, 1996)

A variational principle for computing slow invariant manifolds in dissipative dynamical systems

A key issue in dimension reduction of dissipative dynamical systems with spectral gaps is the identification of slow invariant manifolds. We present theoretical and numerical results for a variational approach to the problem of computing such manifolds for kinetic models using trajectory optimization. The corresponding objective functional reflects a variational principle that characterizes trajectories on, respectively near, slow invariant manifolds. For a two-dimensional linear system and a common nonlinear test problem we show analytically that the variational approach asymptotically identifies the exact slow invariant manifold in the limit of both an infinite time horizon of the variational problem with fixed spectral gap and infinite spectral gap with a fixed finite time horizon. Numerical results for the linear and nonlinear model problems as well as a more realistic higher-dimensional chemical reaction mechanism are presented.Comment: 16 pages, 5 figure