Conservative fourth-order time integration of non-linear dynamic systems

Fourth Order Conservative Exponential Methods for Linear Evolution Equations

A few numerical methods for linear evolution equations are developed and analyzed in this paper. These fourth order methods allow large step sizes for highly oscillatory equations when the evolution operators vary slowly in time. The methods are also conservative for equations such as the Schrr odinger equation, where the evolution operator is skew-selfadjoint.

First order linear fuzzy dynamic equations on time scales

In this paper, we study the concept of generalized differentiability for fuzzy-valued functions on time scales. Usingthe derivative of the product of two functions, we provide solutions to first order linear fuzzy dynamic equations. Wepresent some examples to illustrate our results.

New family of Two-Parameters Iterative Methods for Non-Linear Equations with Fourth-Order Convergence

Fourth Order Conservative Twist Systems: Simple Closed Characteristics

On the energy manifolds of fourth order conservative systems closed characteristics can be found inmany cases via analogues of Twist-maps. The ‘Twist property’ implies the existence of a generating function which leads to second order recurrence relations. We study these recurrence relations to find simple closed characteristics andwe give conditionswhen fourth order systems satisfy the ‘Twist ...

Fourth-order Symplectic Integration*

In this paper we present an explicit fourth-order method for the integration of Hamilton’s Equations. This method preserves the property that the time evolution of such a system yields a canonical transformation from the initial conditions to the final state. That is, the integration step is an explicit symplectic map. Although the result is first derived for a specific type of Hamiltonian, it ...