Numerical comparison of methods for solving second-order ordinary initial value problems
In this paper, we apply Adomian decomposition method (shortly, ADM) to develop a fast and accurate algorithm of a special second-order ordinary initial value problems. The ADM does not require discretization and consequently of massive computations. This paper is particularly concerned with the ADM...
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| Published in: | Applied mathematical modelling Vol. 31; no. 2; pp. 292 - 301 |
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| Format: | Journal Article |
| Language: | English |
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01.02.2007
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| Abstract | In this paper, we apply Adomian decomposition method (shortly, ADM) to develop a fast and accurate algorithm of a special second-order ordinary initial value problems. The ADM does not require discretization and consequently of massive computations. This paper is particularly concerned with the ADM and the results obtained are compared with previously known results using the Quintic
C
2-spline integration methods. The numerical results demonstrate that the ADM is relatively accurate and easily implemented. |
|---|---|
| AbstractList | In this paper, we apply Adomian decomposition method (shortly, ADM) to develop a fast and accurate algorithm of a special second-order ordinary initial value problems. The ADM does not require discretization and consequently of massive computations. This paper is particularly concerned with the ADM and the results obtained are compared with previously known results using the Quintic C2-spline integration methods. The numerical results demonstrate that the ADM is relatively accurate and easily implemented. In this paper, we apply Adomian decomposition method (shortly, ADM) to develop a fast and accurate algorithm of a special second-order ordinary initial value problems. The ADM does not require discretization and consequently of massive computations. This paper is particularly concerned with the ADM and the results obtained are compared with previously known results using the Quintic C 2-spline integration methods. The numerical results demonstrate that the ADM is relatively accurate and easily implemented. |
| Author | Al-Khaled, Kamel Anwar, M. Naim |
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| Cites_doi | 10.1016/S0377-0427(99)00174-0 10.1108/eb005812 10.1016/S0096-3003(99)00063-6 10.1006/jsvi.1996.0445 10.1016/S0898-1221(01)00321-2 10.1016/S0377-0427(03)00473-4 10.1007/BF01933194 10.1016/0895-7177(93)90233-O 10.1016/S0096-3003(01)00021-2 10.1016/0022-247X(88)90170-9 10.1080/00207160211928 10.1016/0898-1221(95)00008-M |
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| Keywords | Quintic spline Adomian decomposition method Approximate solutions Second-order initial value problem Adomian polynomial Modelling Initial value problems Fast algorithm Spline approximation |
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| References | Sallam, Naim Anwar (bib3) 2000; 115 Wazwaz (bib9) 2002; 79 Vigo-Aguiar, Ramos (bib7) 2003; 158 Cherrualt, Adomian (bib11) 1993; 18 Jiao, Yamamoto, Dang, Hao (bib15) 2002; 43 Venkatarangan, Rajalakshmi (bib13) 1995; 29 Baker (bib14) 1975 Adomian (bib1) 1988; 135 Cherrualt (bib10) 1989; 18 Nagle, Saff (bib16) 1994 Semler, Gentleman, Paidoussis (bib6) 1996; 195 Micala (bib4) 1998; 33 Wazwaz (bib8) 2002; 128 Kramarz (bib5) 1980; 20 Wazwaz (bib12) 2000; 111 Adomian (bib2) 1994 Venkatarangan (10.1016/j.apm.2005.11.004_bib13) 1995; 29 Cherrualt (10.1016/j.apm.2005.11.004_bib11) 1993; 18 Nagle (10.1016/j.apm.2005.11.004_bib16) 1994 Cherrualt (10.1016/j.apm.2005.11.004_bib10) 1989; 18 Adomian (10.1016/j.apm.2005.11.004_bib1) 1988; 135 Jiao (10.1016/j.apm.2005.11.004_bib15) 2002; 43 Sallam (10.1016/j.apm.2005.11.004_bib3) 2000; 115 Semler (10.1016/j.apm.2005.11.004_bib6) 1996; 195 Micala (10.1016/j.apm.2005.11.004_bib4) 1998; 33 Adomian (10.1016/j.apm.2005.11.004_bib2) 1994 Kramarz (10.1016/j.apm.2005.11.004_bib5) 1980; 20 Wazwaz (10.1016/j.apm.2005.11.004_bib9) 2002; 79 Wazwaz (10.1016/j.apm.2005.11.004_bib12) 2000; 111 Vigo-Aguiar (10.1016/j.apm.2005.11.004_bib7) 2003; 158 Baker (10.1016/j.apm.2005.11.004_bib14) 1975 Wazwaz (10.1016/j.apm.2005.11.004_bib8) 2002; 128 |
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| SubjectTerms | Adomian decomposition method Approximate solutions Exact sciences and technology Mathematical methods in physics Numerical approximation and analysis Ordinary and partial differential equations, boundary value problems Physics Quintic spline Second-order initial value problem |
| Title | Numerical comparison of methods for solving second-order ordinary initial value problems |
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