27 citations · 70 across the 4 of their papers we have counts for
5 papers
Energy-preserving numerical schemes of high accuracy for one-dimensional Hamiltonian systems
Jan L. Cieśliński, Bogusław Ratkiewicz
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).…
Discrete gradient algorithms of high order for one-dimensional systems
Jan L. Cieśliński, Bogusław Ratkiewicz
We show how to increase the order of one-dimensional discrete gradient numerical integrator without losing its advantages, such as exceptional stability, exact conservation of the…
How to improve the accuracy of the discrete gradient method in the one-dimensional case
Jan L. Cieslinski, Boguslaw Ratkiewicz
We present a new numerical scheme for one dimensional dynamical systems. This is a modification of the discrete gradient method and keeps its advantages, including the stability an…
Long-time behaviour of discretizations of the simple pendulum equation
J. L. Cieslinski, B. Ratkiewicz
We compare the performance of several discretizations of the simple pendulum equation in a series of numerical experiments. The stress is put on the long-time behaviour. We choose…
On simulations of the classical harmonic oscillator equation by difference equations
Jan L. Cieslinski, Boguslaw Ratkiewicz
We show that any second order linear ordinary diffrential equation with constant coefficients (including the damped and undumped harmonic oscillator equation) admits an exact discr…