The population migration algorithm (PMA) is a simulation of a population of the intelligent algorithm. Given the prematurity and low precision of PMA, this paper introduces a local search mechanism of the leap-frog algorithm and crossover operator to improve the PMA search speed and global convergence properties. The typical test function verifies the improved algorithm through its performance....

We present a class of non-standard numerical schemes which are modifications of the discrete gradient method. They preserve the energy integral exactly (up to the round-off error). The considered class contains locally exact discrete gradient schemes and integrators of arbitrary high order. In numerical experiments we compare our integrators with some other numerical schemes, including the stan...

Abstract. We consider second order explicit and implicit two-step time-discrete schemes for wave-type equations. We derive optimal order a posteriori estimates controlling the time discretization error. Our analysis has been motivated by the need to provide a posteriori estimates for the popular leap-frog method (also known as Verlet’s method in the molecular dynamics literature); it is extende...

In this study, the numerical solution for the Modified Equal Width Wave (MEW) equation is presented using Fourier spectral method that use to discretize the space variable and Leap-frog method scheme for time dependence. Test problems including the single soliton wave motion, interaction of two solitary waves and interaction of three solitary waves will use to validate the proposed method. The ...

An efficient and accurate numerical scheme is proposed, analyzed and implemented for the Kawahara and modified Kawahara equations which model many physical phenomena such as gravity-capillary waves and magneto-sound propagation in plasmas. The scheme consists of dual-Petrov-Galerkin method in space and Crank-Nicholson-leap-frog in time such that at each time step only a sparse banded linear sys...

Nonlinear wave motion in dispersive media is solved numerically. The model applies to laser propagation in a relativistic plasma. The latter causes, besides dispersion, nonlinear effects due to relativistic mass variation in the presence of strong laser pulses. A new variant of the Gautschi–type integrator for reducing the number of time steps is proposed as a fast solver for such nonlinear wav...

Given the expressive power of hybrid games, our goal is to explore how easy it is to model realistic games and what insights can be gained from these models. We explore three children’s games (Red Rover, Leap Frog and Red Light, Green Light) to provide examples of interesting multi-player, sometimes collaborative games. Throughout the modeling process we show what is easy to model and what is d...

In this work we study Crank-Nicolson Leap-Frog (CNLF) methods with fast slow wave splittings for Navier-Stokes equation plus a Coriolis force term, which is a simplification of geophysical flows. We present a new stabilized CNLF method where the added stabilization completely removes the method’s CFL time step condition. We give a comprehensive stability and error analysis. We prove that for Os...

This paper reviews the main features of a high-order nondissipative discontinuous Galerkin (DG) method recently investigated in [1]-[3] for solving Maxwell’s equations on non-conforming simplex meshes. The proposed method combines a centered approximation for the numerical fluxes at inter element boundaries, with either a secondorder or a fourth-order leap-frog time integration scheme. Moreover...

We propose a novel class of arbitrarily high-order mass or energy conservative numerical schemes for the generalized Benjamin–Ono equation on whole real line. The spatial discretization is achieved by pseudo-spectral method with rational basis functions. By reformulating discretized system into different equivalent forms, either semi-discretized can be preserved exactly under continuous time fl...