The stability of symplectic algorithms is discussed in this paper. There are following conclusions. 1. Symplectic Runge-Kutta methods and symplectic one-step methods with high order derivative are ...

PageRank is a foundational algorithm that has significantly influenced the way search engines rank webpages by assessing both the quantity and quality of inbound links. The technique, originally ...

This paper is concerned with numerical stability of nonlinear systems of pantograph equations. Numerical methods based on (k,l)—algebraically stable Runge-Kutta methods are suggested. Global and ...

A new scientific approach uses a model inspired from Google's algorithm to determine the degree of stability of the planetary systems. The researchers employed a machine learning technique in order to ...

General aspects of polynomial interpolation theory. Formulations in different basis, e.g. Lagrange, Newton etc. and their approximation and computational properties ...

Optical systems employ a rich array of physical effects which are described by well-understood equations. However, for all but the simplest devices these equations are typically too complex to permit ...