We investigate Hamiltonian systems with two degrees of freedom by using renormalization group method. We show that the original Hamiltonian systems and the renormalization group equations are integrable if the renormalization group equations are Hamiltonian systems up to the second leading order of small parameter. To understand temporal evolutions of Hamiltonian systems, one useful method is t...

the problem of propagation of plane wave including body and surface waves propagating in a transversely isotropic half-space with a depth-wise axis of material symmetry is investigated in details. using the advantage of representation of displacement fields in terms of two complete scalar potential functions, the coupled equations of motion are uncoupled and reduced to two independent equations...

Equations for target height estimation designed for easy use in the Australian growth clinics are presented that are based on the standard deviation score method of Hermanussen and Cole. These equations are superior to the commonly used corrected midparental height method as they account for assortative mating and regression to the mean. Simulations using different mating types were performed t...

Hill’s equations are an approximation that is useful in a number of areas of astrophysics including planetary rings and planetesimal disks. We derive a symplectic method for integrating Hill’s equations based on a generalized leapfrog. This method is implemented in the parallel N -body code, PKDGRAV and tested on some simple orbits. The method demonstrates a lack of secular changes in orbital e...

We apply the Lindstedt method to the one dimensional Fermi-Pasta-Ulam β lattice to find fully general solutions to the complete set of equations of motion. The pertubative scheme employed uses ǫ as the expansion parameter, where ǫ is the coefficient of the quartic coupling between nearest neighbors. We compare our non-secular perturbative solutions to numerical solutions and find striking agree...

Traditional explicit numerical discretizations of conservative systems generically predict arti cial secular drifts of nonlinear invariants. These algorithms are based on polynomial functions of the time step. We discuss a general approach for developing explicit algorithms that conserve such invariants exactly. We illustrate the method by applying it to the truncated two-dimensional Euler equa...

In this paper we develop a hybrid symbolic-numeric fast method for solving the secular equation associated with a diagonal plus rank-one eigenvalue problem of order n in O(n) operations and O(n) storage. AMS classification: 65F15

In this work, the behaviour of magneto-hydrodynamic waves in optically thin plasmas considering dissipative processes, thermal and magnetic diffusion, a given ionization, heating cooling functions are investigated for several particular cases. A numerical eigenvalues analysis dimensionless secular equations according to various cases is performed entire set MHD equations.