## Improved Precision of Numerical Integration for Equations of Motion of Asteroids and Comets

Transactions of IAA RAS, issue 43, 70–77 (2017)

**Keywords**:
numerical integration, Encke method, Fortran, precision of integration

### Abstract

We have modified the Encke Method for numerical integration of differential equations of motion of asteroids and comets. The numerical solution is considered as a sum of the approximate solution and a small term representing the deviation from the approximate solution. The Taylor polynomial in power of time is taken as the approximation, which is calculated with multiple accuracy. The differential equation is written for the small term and the term is computed by integration the differential equation with ordinary precision. The integration step is chosen so that the term is less than a certain value. This approach allows us to increase the precision of numerical integration without significantly increasing the integration time.

### Citation

`A. P. Ershova, Yu. D. Medvedev, D. E. Vavilov. Improved Precision of Numerical Integration for Equations of Motion of Asteroids and Comets // Transactions of IAA RAS. — 2017. — Issue 43. — P. 70–77.`

```
@article{ershova2017,
abstract = {We have modified the Encke Method for numerical integration of differential equations of motion of asteroids and comets. The numerical solution is considered as a sum of the approximate solution and a small term representing the deviation from the approximate solution. The Taylor polynomial in power of time is taken as the approximation, which is calculated with multiple accuracy. The differential equation is written for the small term and the term is computed by integration the differential equation with ordinary precision. The integration step is chosen so that the term is less than a certain value. This approach allows us to increase the precision of numerical integration without significantly increasing the integration time.},
author = {A.~P. Ershova and Yu.~D. Medvedev and D.~E. Vavilov},
issue = {43},
journal = {Transactions of IAA RAS},
keyword = {numerical integration, Encke method, Fortran, precision of integration},
pages = {70--77},
title = {Improved Precision of Numerical Integration for Equations of Motion of Asteroids and Comets},
url = {http://iaaras.ru/en/library/paper/1766/},
year = {2017}
}
```

```
TY - JOUR
TI - Improved Precision of Numerical Integration for Equations of Motion of Asteroids and Comets
AU - Ershova, A. P.
AU - Medvedev, Yu. D.
AU - Vavilov, D. E.
PY - 2017
T2 - Transactions of IAA RAS
IS - 43
SP - 70
AB - We have modified the Encke Method for numerical integration of
differential equations of motion of asteroids and comets. The
numerical solution is considered as a sum of the approximate solution
and a small term representing the deviation from the approximate
solution. The Taylor polynomial in power of time is taken as the
approximation, which is calculated with multiple accuracy. The
differential equation is written for the small term and the term is
computed by integration the differential equation with ordinary
precision. The integration step is chosen so that the term is less
than a certain value. This approach allows us to increase the
precision of numerical integration without significantly increasing
the integration time.
UR - http://iaaras.ru/en/library/paper/1766/
ER -
```