CALCULATION SCHEMES EFFICIENCY FOR INTEGRATION OF ORDINARY DIFFERENTIAL EQUATIONS BASED ON THE DIFFERENTIAL-TAYLOR TRANSFORMATION
The theoretical evaluation of the effectiveness of explicit computational schemes for numerical solution of the Cauchy problem for ordinary differential equations are given, which are based on differential-taylor transformations in comparison with the schemes that have been developed on the basis of...
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| Format: | Article |
| Language: | English |
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National Defence University of Ukraine named after Ivan Cherniakhovsky
2014-09-01
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| Series: | Sučasnì Informacìjnì Tehnologìï u Sferì Bezpeki ta Oboroni |
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| Online Access: | http://sit.nuou.org.ua/article/view/34642 |
| _version_ | 1818473184453722112 |
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| author | Yurii V. Kravchenko Mykhailo Y. Rakushev Yevhen O. Sudnikov Igor V. Ushakov |
| author_facet | Yurii V. Kravchenko Mykhailo Y. Rakushev Yevhen O. Sudnikov Igor V. Ushakov |
| author_sort | Yurii V. Kravchenko |
| collection | DOAJ |
| description | The theoretical evaluation of the effectiveness of explicit computational schemes for numerical solution of the Cauchy problem for ordinary differential equations are given, which are based on differential-taylor transformations in comparison with the schemes that have been developed on the basis of the Adams predictor-corrector scheme. The effectiveness of the computational schemes is evaluated by comparing the required computational costs while maintaining a specified accuracy of the calculation. On the basis of these estimates practical recommendations on the effectiveness of the method of differential-taylor transformations for numerical integration of ordinary differential equations. It is shown that the overall efficiency of the method of differential-taylor transformation increases with an increase in the required accuracy of integration (reducing local integration error) ordinary differential equation. |
| first_indexed | 2024-04-14T04:19:51Z |
| format | Article |
| id | doaj.art-878f978934f845b2b8bc72fa62c72a8d |
| institution | Directory Open Access Journal |
| issn | 2311-7249 2410-7336 |
| language | English |
| last_indexed | 2024-04-14T04:19:51Z |
| publishDate | 2014-09-01 |
| publisher | National Defence University of Ukraine named after Ivan Cherniakhovsky |
| record_format | Article |
| series | Sučasnì Informacìjnì Tehnologìï u Sferì Bezpeki ta Oboroni |
| spelling | doaj.art-878f978934f845b2b8bc72fa62c72a8d2022-12-22T02:12:35ZengNational Defence University of Ukraine named after Ivan CherniakhovskySučasnì Informacìjnì Tehnologìï u Sferì Bezpeki ta Oboroni2311-72492410-73362014-09-0102(20)657434642CALCULATION SCHEMES EFFICIENCY FOR INTEGRATION OF ORDINARY DIFFERENTIAL EQUATIONS BASED ON THE DIFFERENTIAL-TAYLOR TRANSFORMATIONYurii V. Kravchenko0Mykhailo Y. Rakushev1Yevhen O. Sudnikov2Igor V. Ushakov3State University of TelecommunicationsNational Defence University of Ukraine named after Ivan CherniakhovskyNational Defence University of Ukraine named after Ivan CherniakhovskyNational Defence University of Ukraine named after Ivan CherniakhovskyThe theoretical evaluation of the effectiveness of explicit computational schemes for numerical solution of the Cauchy problem for ordinary differential equations are given, which are based on differential-taylor transformations in comparison with the schemes that have been developed on the basis of the Adams predictor-corrector scheme. The effectiveness of the computational schemes is evaluated by comparing the required computational costs while maintaining a specified accuracy of the calculation. On the basis of these estimates practical recommendations on the effectiveness of the method of differential-taylor transformations for numerical integration of ordinary differential equations. It is shown that the overall efficiency of the method of differential-taylor transformation increases with an increase in the required accuracy of integration (reducing local integration error) ordinary differential equation.http://sit.nuou.org.ua/article/view/34642differential-taylor transformationcauchy problemcomputational scheme |
| spellingShingle | Yurii V. Kravchenko Mykhailo Y. Rakushev Yevhen O. Sudnikov Igor V. Ushakov CALCULATION SCHEMES EFFICIENCY FOR INTEGRATION OF ORDINARY DIFFERENTIAL EQUATIONS BASED ON THE DIFFERENTIAL-TAYLOR TRANSFORMATION Sučasnì Informacìjnì Tehnologìï u Sferì Bezpeki ta Oboroni differential-taylor transformation cauchy problem computational scheme |
| title | CALCULATION SCHEMES EFFICIENCY FOR INTEGRATION OF ORDINARY DIFFERENTIAL EQUATIONS BASED ON THE DIFFERENTIAL-TAYLOR TRANSFORMATION |
| title_full | CALCULATION SCHEMES EFFICIENCY FOR INTEGRATION OF ORDINARY DIFFERENTIAL EQUATIONS BASED ON THE DIFFERENTIAL-TAYLOR TRANSFORMATION |
| title_fullStr | CALCULATION SCHEMES EFFICIENCY FOR INTEGRATION OF ORDINARY DIFFERENTIAL EQUATIONS BASED ON THE DIFFERENTIAL-TAYLOR TRANSFORMATION |
| title_full_unstemmed | CALCULATION SCHEMES EFFICIENCY FOR INTEGRATION OF ORDINARY DIFFERENTIAL EQUATIONS BASED ON THE DIFFERENTIAL-TAYLOR TRANSFORMATION |
| title_short | CALCULATION SCHEMES EFFICIENCY FOR INTEGRATION OF ORDINARY DIFFERENTIAL EQUATIONS BASED ON THE DIFFERENTIAL-TAYLOR TRANSFORMATION |
| title_sort | calculation schemes efficiency for integration of ordinary differential equations based on the differential taylor transformation |
| topic | differential-taylor transformation cauchy problem computational scheme |
| url | http://sit.nuou.org.ua/article/view/34642 |
| work_keys_str_mv | AT yuriivkravchenko calculationschemesefficiencyforintegrationofordinarydifferentialequationsbasedonthedifferentialtaylortransformation AT mykhailoyrakushev calculationschemesefficiencyforintegrationofordinarydifferentialequationsbasedonthedifferentialtaylortransformation AT yevhenosudnikov calculationschemesefficiencyforintegrationofordinarydifferentialequationsbasedonthedifferentialtaylortransformation AT igorvushakov calculationschemesefficiencyforintegrationofordinarydifferentialequationsbasedonthedifferentialtaylortransformation |