n-Step n + 2th order stable method for linear ordinary differential equations

Author

Solopov, Valery

Author_Institution

Moscow State Univ. of Instrum. Eng. & Comput. Sci., Moscow, Russia

fYear

2015

fDate

2-6 Feb. 2015

Firstpage

1

Lastpage

5

Abstract

The families of the n-step methods of order n + 2 for systems of linear differential equations of the 1st order are built for even n≥4. The stability domains of the methods are found. A comparison with the Runge-Kutta 4th order method and the Dorman-Prince 8th order method was made. Numerical experiment on the model examples showed that the computation time for solving the problem can be reduced by hundreds of times for the mean-square error about 10^-13-10^-14 that is an important factor in the resolving laborious numerical problems in mechanics. Also carried out a comparison with the Magnus method, specialized for linear differential equations. Areas in which each of the methods has its advantages to be determined.

Keywords

Runge-Kutta methods; linear differential equations; mean square error methods; numerical stability; Dorman-Prince 8th order method; Magnus method; Runge-Kutta 4th order method; computation time; linear ordinary differential equations; mean-square error; n-step n+2th order stable method; numerical experiment; numerical problems; stability domains; Differential equations; Mathematical model; Numerical stability; Oscillators; Polynomials; Stability analysis; Standards;

fLanguage

English

Publisher

ieee

Conference_Titel

Mechanics - Seventh Polyakhov's Reading, 2015 International Conference on

Conference_Location

Saint Petersburg

Type

conf

DOI

10.1109/POLYAKHOV.2015.7106781

Filename

7106781