New 4(3) Pairs Diagonally Implicit Runge-Kutta-Nyström Method for Periodic IVPs
New 4(3) pairs Diagonally Implicit Runge-Kutta-Nyström (DIRKN) methods with reduced phase-lag are developed for the integration of initial value problems for second-order ordinary differential equations possessing oscillating solutions. Two DIRKN pairs which are three- and four-stage with high order...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2012/324989 |
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| _version_ | 1832556974292598784 |
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| author | Norazak Senu Mohamed Suleiman Fudziah Ismail Norihan Md Arifin |
| author_facet | Norazak Senu Mohamed Suleiman Fudziah Ismail Norihan Md Arifin |
| author_sort | Norazak Senu |
| collection | DOAJ |
| description | New 4(3) pairs Diagonally Implicit Runge-Kutta-Nyström (DIRKN) methods with reduced phase-lag are developed for the integration of initial value problems for second-order ordinary differential equations possessing oscillating solutions. Two DIRKN pairs which are three- and four-stage with high order of dispersion embedded with the third-order formula for the estimation of the local truncation error. These new methods are more efficient when compared with current methods of similar type and with the L-stable Runge-Kutta pair derived by Butcher and Chen (2000) for the numerical integration of second-order differential equations with periodic solutions. |
| format | Article |
| id | doaj-art-b2bc75b4062a418e97ba3a9a0efbafdd |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-b2bc75b4062a418e97ba3a9a0efbafdd2025-02-03T05:44:02ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2012-01-01201210.1155/2012/324989324989New 4(3) Pairs Diagonally Implicit Runge-Kutta-Nyström Method for Periodic IVPsNorazak Senu0Mohamed Suleiman1Fudziah Ismail2Norihan Md Arifin3Department of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor, MalaysiaDepartment of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor, MalaysiaDepartment of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor, MalaysiaDepartment of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor, MalaysiaNew 4(3) pairs Diagonally Implicit Runge-Kutta-Nyström (DIRKN) methods with reduced phase-lag are developed for the integration of initial value problems for second-order ordinary differential equations possessing oscillating solutions. Two DIRKN pairs which are three- and four-stage with high order of dispersion embedded with the third-order formula for the estimation of the local truncation error. These new methods are more efficient when compared with current methods of similar type and with the L-stable Runge-Kutta pair derived by Butcher and Chen (2000) for the numerical integration of second-order differential equations with periodic solutions.http://dx.doi.org/10.1155/2012/324989 |
| spellingShingle | Norazak Senu Mohamed Suleiman Fudziah Ismail Norihan Md Arifin New 4(3) Pairs Diagonally Implicit Runge-Kutta-Nyström Method for Periodic IVPs Discrete Dynamics in Nature and Society |
| title | New 4(3) Pairs Diagonally Implicit Runge-Kutta-Nyström Method for Periodic IVPs |
| title_full | New 4(3) Pairs Diagonally Implicit Runge-Kutta-Nyström Method for Periodic IVPs |
| title_fullStr | New 4(3) Pairs Diagonally Implicit Runge-Kutta-Nyström Method for Periodic IVPs |
| title_full_unstemmed | New 4(3) Pairs Diagonally Implicit Runge-Kutta-Nyström Method for Periodic IVPs |
| title_short | New 4(3) Pairs Diagonally Implicit Runge-Kutta-Nyström Method for Periodic IVPs |
| title_sort | new 4 3 pairs diagonally implicit runge kutta nystrom method for periodic ivps |
| url | http://dx.doi.org/10.1155/2012/324989 |
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