Adaptive methods for second order initial value problems

Sesappa A. Rai

Research output: Contribution to journalConference article

Abstract

This paper deals with two-step methods of order two and order four with minimum truncation error for numerical integration of second order initial value problems. The methods depend upon a parameter p>0, and reduce to the Classical Numerov method for p=0. As p becomes very large the truncation error tends to zero. The methods are unconditionally stable when applied to the test equation. To illustrate the order, accuracy and stability of the method, the test problem and non linear undamped duffing equations are solved. The results are compared with some other well known methods and the derived methods give better results than any other existing fourth order methods.

Original languageEnglish
Pages (from-to)639-643
Number of pages5
JournalAIP Conference Proceedings
Volume1281
DOIs
Publication statusPublished - 01-12-2010
Externally publishedYes
EventInternational Conference on Numerical Analysis and Applied Mathematics 2010, ICNAAM-2010 - Rhodes, Greece
Duration: 19-09-201025-09-2010

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truncation errors
boundary value problems
numerical integration

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

Cite this

Rai, Sesappa A. / Adaptive methods for second order initial value problems. In: AIP Conference Proceedings. 2010 ; Vol. 1281. pp. 639-643.
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Adaptive methods for second order initial value problems. / Rai, Sesappa A.

In: AIP Conference Proceedings, Vol. 1281, 01.12.2010, p. 639-643.

Research output: Contribution to journalConference article

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AB - This paper deals with two-step methods of order two and order four with minimum truncation error for numerical integration of second order initial value problems. The methods depend upon a parameter p>0, and reduce to the Classical Numerov method for p=0. As p becomes very large the truncation error tends to zero. The methods are unconditionally stable when applied to the test equation. To illustrate the order, accuracy and stability of the method, the test problem and non linear undamped duffing equations are solved. The results are compared with some other well known methods and the derived methods give better results than any other existing fourth order methods.

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