76 citations · 631 across the 35 of their papers we have counts for
6 papers · 1 filter
Conjugate-symplecticity properties of Euler--Maclaurin methods and their implementation on the Infinity Computer
F. Iavernaro, F. Mazzia, M. S. Mukhametzhanov +1
Multi-derivative one-step methods based upon Euler-Maclaurin integration formulae are considered for the solution of canonical Hamiltonian dynamical systems. Despite the negative r…
Solving ordinary differential equations on the Infinity Computer by working with infinitesimals numerically
Yaroslav D. Sergeyev
There exists a huge number of numerical methods that iteratively construct approximations to the solution of an ordinary differential equation (ODE) starting…
Methodology of Numerical Computations with Infinities and Infinitesimals
Yaroslav D. Sergeyev
A recently developed computational methodology for executing numerical calculations with infinities and infinitesimals is described in this paper. The developed approach has a pron…
Higher order numerical differentiation on the Infinity Computer
Yaroslav D. Sergeyev
There exist many applications where it is necessary to approximate numerically derivatives of a function which is given by a computer procedure. In particular, all the fields of op…
Numerical computations and mathematical modelling with infinite and infinitesimal numbers
Yaroslav D. Sergeyev
Traditional computers work with finite numbers. Situations where the usage of infinite or infinitesimal quantities is required are studied mainly theoretically. In this paper, a re…
Two methods for solving optimization problems arising in electronic measurements and electrical engineering
Yaroslav D. Sergeyev, Pasquale Daponte, Domenico Grimaldi +1
In this paper we introduce a common problem in electronic measurements and electrical engineering: finding the first root from the left of an equation in the presence of some initi…