In this paper we study the performance of a symplectic numerical integrator based on the splitting method. This method is applied to a subtle problem i.e. higher order resonance of the elastic pendulum. In order to numerically study the phase space of the elastic pendulum at higher order resonance, a numerical integrator which preserves qualitative features after long integration times is neede...

The standard hybrid Monte Carlo algorithm uses the second order integrator at the molecular dynamics step. This choice of the integrator is not always the best. We study the performance of the hybrid Monte Carlo algorithm for lattice QCD with higher order integrators in both zero and finite temperature phases and find that in the finite temperature phase the performance of the algorithm can be ...

continuous stirred tank reactor (cstr) has particular importance in chemical industry. cstr has usually a nonlinear behavior which makes it difficult to control. the reactor has two parameters: the concentration and temperature of mixture both of which are uncertain. this case of cstr has large disturbance in domain. in order for disturbance rejection, a controller has to be designed. in this p...

A variable-step double-integration multi-step integrator is derived using divided differences. The derivation is based upon the derivation of Shampine-Gordon, a single-integration method. Variable-step integrators are useful for propagating elliptical orbits, because larger steps can be taken near apogee. As a double-integration method, the integrator performs only one function evaluation per s...

A multiscale fatigue analysis model is developed for brittle composite materials. The mathematical homogenization theory is generalized to account for multiscale damage effects in heterogeneous media and a closed form expression relating nonlocal microphase fields to the overall strains and damage is derived. The evolution of fatigue damage is approximated by the first order initial value probl...

This paper deals with a new Henstock-Kurzweil integral in Banach Space Bilinear triple n-tuple and integrator function Ψ which depends on multiple points partition. Finally, exhibit standard results of Generalized Henstock - Kurzweil the theory integration.