99 citations · 459 across the 24 of their papers we have counts for
7 papers · 1 filter
Improving the accuracy of the fast inverse square root algorithm
Cezary J. Walczyk, Leonid V. Moroz, Jan L. Cieśliński
We present improved algorithms for fast calculation of the inverse square root for single-precision floating-point numbers. The algorithms are much more accurate than the famous fa…
Improving the accuracy of the AVF method
Jan L. Cieśliński
The Average Vector Field (AVF) method is a B-series scheme of the second order. As a discrete gradient method it preserves exactly the energy integral for any canonical Hamiltonian…
Locally exact modifications of numerical schemes
Jan L. Cieśliński
We present a new class of exponential integrators for ordinary differential equations: locally exact modifications of known numerical schemes. Local exactness means that they prese…
Locally exact modifications of numerical integrators
Jan L. Cieśliński
We present a new class of exponential integrators for ordinary differential equations. They are locally exact, i.e., they preserve the linearization of the original system at every…
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).…
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…