Symplectic Runge-Kutta-Nystr?m Methods with Phase-Lag Oder 8 and Infinity

In this work we consider Symplectic Runge Kutta Nystr¨om methods with five stages. A new fourth algebraic order method with phase-lag order eight is presented. Also the symplectic Runge Kutta Nystr¨om of Calvo and Sanz Serna with five stages and fourth order is modified to produce a phase-fitted method. We apply the new methods on several Hamiltonian systems and on the computation of the eigenvalues of the Schr¨odinger Equation

Computational method for approximating the behaviour of a triopoly: An application to the mobile telecommunications sector in Greece

Computational biology models of the Volterra-Lotka family, known as competing species models, are used for modelling a triopoly market, with application to the mobile telecommunications in Greece. Using a data sample for 1999–2016, parameter estimation with nonlinear least squares is performed. The findings show that the proportional change in the market share of the two largest companies, Cosmote and Vodafone, depends negatively on the market share of each other. Further, the market share of the marker leader, Cosmote, depends positively on the market share of the smallest company, Wind. The proportional change in the market share of Wind, depends negatively on the market share of the largest company Cosmote but it depends positively by the change in the market share by the second company, Vodafone. In the long-run it was found that the market shares tend to the stable equilibrium point where all three companies will survive with Cosmote having a projected number after eleven years (in 2030) of approximately 7.3 million subscribers, Vodafone 4.9 and Wind 3.7, the total number of projected market size being approximately 16 million customers. Copyright © 2021 Inderscience Enterprises Ltd

Construction of exponentially fitted symplectic Runge-Kutta-Nyström methods from partitioned Runge-Kutta methods

In this work we derive exponentially fitted symplectic Runge-Kutta-Nystr¨om (RKN) methods from symplectic exponentially fitted partitioned Runge-Kutta (PRK) methods methods. We construct RKN methods from PRK methods with up to five stages and fourth algebraic order

Application of bi-Helmholtz nonlocal elasticity and molecular simulations to the dynamical response of carbon nanotubes

The nonlocal theory of elasticity is employed for the study of the free vibrations of carbon nanotubes (CNT). For the first time, a bi-Helmholtz operator has been used instead of the standard Helmholtz operator in a nonlocal beam model. Alongside the continuum formulation and its numerical solution, atomistic Molecular Dynamics (MD) simulations have been conducted in order to directly evaluate the eigenfrequencies of vibrating CNTs with a minimum of adjustable parameters. Our results show that the bi-Helmholtz operator is the most appropriate one to fit MD simulation results. However, the estimation of vibration eigenfrequencies from molecular simulations still remains an open (albeit well-posed) problem