arXiv subjects

Alexey S. Eremin

Publications and source records attributed to Alexey S. Eremin.

2 recordsLinked to original sources

arXiv2018

Functional Continuous Runge-Kutta Methods with Reuse

In the paper explicit functional continuous Runge-Kutta and Runge-Kutta-Nyström methods for retarded functional differential equations are considered. New methods for first order equations as well as for second order equations of the special form are constructed with the reuse of the last stage of the step. The order conditions for Runge-Kutta-Nyström methods are derived. Methods of orders three, four and five which require less computations than the known methods are presented. Numerical solution of the test problems confirm the convergence order of the new methods and their lower computational cost is performed.

math.NA↗

arXiv2017

Solving Boundary Value Problem for a Nonlinear Stationary Controllable System with Synthesizing Control

An algorithm for constructing a control function that transfers a wide class of stationary nonlinear systems of ordinary differential equations from an initial state to a final state under certain control restrictions is proposed. The algorithm is designed to be convenient for numerical implementation. A constructive criterion of the desired transfer possibility is presented. The problem of an interorbital flight is considered as a test example and it is simulated numerically with the presented method.

math.OC↗