New modified Runge–Kutta–Nyström methods for the numerical integration of the Schrödinger equation

AbstractIn this work we construct new Runge–Kutta–Nyström methods especially designed to integrate exactly the test equation y″=−w2y. We modify two existing methods: the Runge–Kutta–Nyström methods of fifth and sixth order. We apply the new methods to the computation of the eigenvalues of the Schrödinger equation with different potentials such as the harmonic oscillator, the doubly anharmonic oscillator and the exponential potential

Exponentially fitted symplectic Runge-Kutta-Nyström methods

In this work we consider symplectic Runge Kutta Nystr¨om (SRKN) methods with three stages. We construct a fourth order SRKN with constant coefficients and a trigonometrically fitted SRKN method. We apply the new methods on the two-dimentional harmonic oscillator, the Stiefel-Bettis problem and on the computation of the eigenvalues of the Schr¨odinger equation

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

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

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

Best Chebyshev approximation from families of ordinary differential equations

SIGLEGBUnited Kingdo

Nonlinear Chebyshev fitting from the solution of ordinary differential equations

SIGLEGBUnited Kingdo

The local Haar condition in parameter estimation for second order ordinary differential equations

SIGLEAvailable from British Library Document Supply Centre-DSC:6184.6725(302) / BLDSC - British Library Document Supply CentreGBUnited Kingdo