Improved error bounds for freezing solutions of linear boundary value problems
For the error in the freezing solutions of linear boundary value problems we obtain a bound which is sharper than that obtained recently by Shahruz and Schwartz [Appl. Math. Comput. 60 (1994) 285; Comput. Math. Appl. 28 (1994) 75]. A different freezing technique, “global freezing”, is also proposed....
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| Vydané v: | Applied mathematics and computation Ročník 94; číslo 2; s. 97 - 112 |
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| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
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New York, NY
Elsevier Inc
15.08.1998
Elsevier |
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| ISSN: | 0096-3003, 1873-5649 |
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| Abstract | For the error in the freezing solutions of linear boundary value problems we obtain a bound which is sharper than that obtained recently by Shahruz and Schwartz [Appl. Math. Comput. 60 (1994) 285; Comput. Math. Appl. 28 (1994) 75]. A different freezing technique, “global freezing”, is also proposed. It is shown that this new technique is easy to implement for numerical computation of the solutions. Moreover, the corresponding solution has an error bound similar to that of the freezing method. |
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| AbstractList | For the error in the freezing solutions of linear boundary value problems we obtain a bound which is sharper than that obtained recently by Shahruz and Schwartz [Appl. Math. Comput. 60 (1994) 285; Comput. Math. Appl. 28 (1994) 75]. A different freezing technique, 'global freezing', is also proposed. It is shown that this new technique is easy to implement for numerical computation of the solutions. Moreover, the corresponding solution has an error bound similar to that of the freezing method. |
| Author | Qu, Ruibin Agarwal, Ravi P. |
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| Cites_doi | 10.1017/S0334270000007578 10.1016/0096-3003(94)90110-4 10.1016/0898-1221(94)00153-7 10.1016/0022-460X(89)90489-6 10.1016/0377-0427(83)90003-1 10.1016/0167-6911(87)90022-3 10.1016/0895-7177(93)90006-K 10.32917/hmj/1206128500 |
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| Keywords | Linear boundary value problems Error estimates Freezing techniques Error analysis Boundary value problem Linear equation Differential equation Numerical solution Partial differential equation |
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| References | Vidyasagar (BIB12) 1993 Shridharan, Agarwal (BIB4) 1993; 18 Desoer, Vidyasagar (BIB8) 1975 Keller (BIB3) 1976; 24 Keller (BIB2) 1968 Ascher, Mattheij, Russell (BIB1) 1988 Ilchmann, Owens, Prátzel-Wolters (BIB10) 1987; 9 Shahruz, Schwartz (BIB14) 1994; 28 Aziz (BIB7) 1975 Horn, Johnson (BIB16) 1985 Shridharan, Agarwal (BIB9) 1995; 37 Fox (BIB15) 1957 Agarwal (BIB5) 1983; 9 Shahruz, Tan (BIB11) 1989; 131 Agarwal (BIB6) 1992; 22 Shahruz, Schwartz (BIB13) 1994; 60 Agarwal (10.1016/S0096-3003(97)10067-4_BIB6) 1992; 22 Keller (10.1016/S0096-3003(97)10067-4_BIB3) 1976; 24 Agarwal (10.1016/S0096-3003(97)10067-4_BIB5) 1983; 9 Ilchmann (10.1016/S0096-3003(97)10067-4_BIB10) 1987; 9 Horn (10.1016/S0096-3003(97)10067-4_BIB16) 1985 Shridharan (10.1016/S0096-3003(97)10067-4_BIB9) 1995; 37 Fox (10.1016/S0096-3003(97)10067-4_BIB15) 1957 Aziz (10.1016/S0096-3003(97)10067-4_BIB7) 1975 Shahruz (10.1016/S0096-3003(97)10067-4_BIB13) 1994; 60 Shridharan (10.1016/S0096-3003(97)10067-4_BIB4) 1993; 18 Shahruz (10.1016/S0096-3003(97)10067-4_BIB14) 1994; 28 Desoer (10.1016/S0096-3003(97)10067-4_BIB8) 1975 Vidyasagar (10.1016/S0096-3003(97)10067-4_BIB12) 1993 Keller (10.1016/S0096-3003(97)10067-4_BIB2) 1968 Ascher (10.1016/S0096-3003(97)10067-4_BIB1) 1988 Shahruz (10.1016/S0096-3003(97)10067-4_BIB11) 1989; 131 |
| References_xml | – volume: 28 start-page: 75 year: 1994 end-page: 82 ident: BIB14 article-title: An approximate solution for homogeneous linear boundary value problems with slowly-varying coefficient matrices publication-title: Comput. Math. Appl. – year: 1993 ident: BIB12 article-title: Nonlinear Systems Analysis – year: 1975 ident: BIB7 article-title: Numerical Solutions of Boundary Value Problems for Ordinary Differential Equations – year: 1957 ident: BIB15 article-title: The Numerical Solution of Two-Point Boundary Problems in Ordinary Differential Equations – year: 1975 ident: BIB8 article-title: Feedback Systems: Input-Output Properties – year: 1968 ident: BIB2 article-title: Numerical Methods for Two-Point Boundary-value Problems – volume: 22 start-page: 525 year: 1992 end-page: 541 ident: BIB6 article-title: Component-wise convergence of quasilinear method for nonlinear boundary value problems publication-title: Hiroshima Math. 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| SubjectTerms | Error analysis Error estimates Exact sciences and technology Freezing techniques Linear boundary value problems Mathematics Numerical analysis Numerical analysis. Scientific computation Ordinary differential equations Partial differential equations, boundary value problems Sciences and techniques of general use |
| Title | Improved error bounds for freezing solutions of linear boundary value problems |
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