In this paper, a multi-step differential transform method (MsDTM) is performed to give approximate and analytical solutions of nonlinear fractional order ordinary differential equation systems such as amodel for HIV infection of CD4 T cells. The numerical solutions obtained from the proposed method indicate that the approach is easy to implement and accurate when applied to systems of fractiona...

Modified Adomian decomposition method has been used intensively to solve linear and nonlinear singular boundary and initial value problems. It has been proved to be very efficient in generating series solutions of the problem under consideration under the assumption that such series solution exits. The method is illustrated by some examples of higher order ordinary equations systems and series ...

Modified Adomian decomposition method has been used intensively to solve linear and nonlinear singular boundary and initial value problems. It has been proved to be very efficient in generating series solutions of the problem under consideration under the assumption that such series solution exits. The method is illustrated by some examples of higher order ordinary equations systems and series ...

Kuramoto-Sivashinsky equation was introduced by Kuramoto [1976] in one-spatial dimension, for the study of phase turbulance in the BelousovZhabotinsky reaction. Sivashinsky derived it independently in the context of small thermal diffusive instabilities for laminar flame fronts. It and related equations have also been used to model directional solidification and , in multiple spatial dimensions...

Several nonlinear three-dimensional systems of ordinary differential equations are studied analytically and numerically in this paper in accordance with universal bifurcation theory of Feigenbaum-Sharkovskii-Magnitsky [1] [2]. All systems are autonomous and dissipative and display chaotic behaviour. The analysis confirms that transition to chaos in such systems is performed through cascades of ...

In this article, the multi-step differential transform method (MsDTM) is applied to give approximate solutions of nonlinear ordinary differential equation such as fractional-non-linear oscillatory and vibration equations. The results indicate that the method is very effective and sufficient for solving nonlinear differential equations of fractional order.

Hybrid cc is a constraint programming language suitable for modeling, controlling and simulating hybrid systems, i.e. systems with continuous and discrete state changes. The language extends the concurrent constraint programming framework with default reasoning and combinators for programming continuous behavior. The most important constraint systems used in Hybrid cc are nonlinear equations an...

The problem of controllability of linear and nonlinear systems represented by ordinary differential equations in finite dimensional spaces has been extensively studied. Several authors [5,6,12-14] have extended the concept to infinite dimensional systems in Banach spaces with bounded operators. Triggiani [17] established sufficient conditions for controllability of linear and nonlinear systems ...

In this study the interaction between self-excited and paramet rically excited oscillations in two-degree-of-freedom systems with quadratic nonlinearities is investigated. The fundamental parametric resonance of the first mode and 3:1 internal resonance is considered, followed by 1:2 internal and parametric resonances of the second mode. The method of multiple time scales is applied to derive f...