Numerical solution of nonlinear singularly perturbed problems by using a non-standard algorithm on variable stepsize implementation (CMMSE–2009)
In this article, we solve numerically singularly perturbed non-linear autonomous initial-value problems (IVPs) by using a non-standard algorithm on a variable stepsize implementation. On a recent article (Ramos et al. in J Math Chem, To appear) we had used nonuniform meshes for resolving the difficu...
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| Published in: | Journal of mathematical chemistry Vol. 48; no. 1; pp. 98 - 108 |
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| Format: | Journal Article Conference Proceeding |
| Language: | English |
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01.07.2010
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| ISSN: | 0259-9791, 1572-8897 |
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| Abstract | In this article, we solve numerically singularly perturbed non-linear autonomous initial-value problems (IVPs) by using a non-standard algorithm on a variable stepsize implementation. On a recent article (Ramos et al. in J Math Chem, To appear) we had used nonuniform meshes for resolving the difficulties arising from the steep gradient of the solution in the initial layer. The present method is intended for solving the nonlinear problem using a nonuniform mesh originated by a suitable strategy provided for changing the stepsize. Numerical experiments are carried out to verify the efficiency and accuracy of the method, showing that the new procedure leads to better results than in (Ramos et al. in J Math Chem, To appear). |
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| AbstractList | In this article, we solve numerically singularly perturbed non-linear autonomous initial-value problems (IVPs) by using a non-standard algorithm on a variable stepsize implementation. On a recent article (Ramos et al. in J Math Chem, To appear) we had used nonuniform meshes for resolving the difficulties arising from the steep gradient of the solution in the initial layer. The present method is intended for solving the nonlinear problem using a nonuniform mesh originated by a suitable strategy provided for changing the stepsize. Numerical experiments are carried out to verify the efficiency and accuracy of the method, showing that the new procedure leads to better results than in (Ramos et al. in J Math Chem, To appear). |
| Author | García-Rubio, R. Ramos, Higinio |
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| Cites_doi | 10.1016/j.cam.2004.12.018 10.1016/0009-2509(68)89005-0 10.1007/BF02144108 10.1016/j.bej.2007.08.003 10.1016/0377-0427(83)90040-7 10.1016/j.amc.2006.11.134 10.1016/0008-6223(96)00010-3 10.1016/j.colsurfa.2008.01.032 10.1080/00207160701199773 10.1016/0377-0427(94)00108-1 10.1038/nature01258 10.1016/j.apm.2007.02.019 10.1021/jp061779n 10.1016/0898-1221(86)90245-2 10.1023/B:SUPE.0000009322.23950.53 10.1016/0898-1221(87)90065-4 10.1007/s10910-009-9625-2 10.1016/0009-2509(69)80017-5 10.1007/978-3-662-12607-3 10.1142/2933 |
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| Keywords | Nonuniform meshes Singularly perturbed initial-value problems Non-standard algorithm Variable stepsize implementation Mathematical chemistry Grid pattern Initial value problem Nonlinear problems Algorithm Layer Implementation Standards Efficiency Numerical solution Singularly perturbed initial-value problem Problem solving |
| Language | English |
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| References | Danish, Sharma, Ali (CR5) 2008; 32 Rudzinski, Plazinski (CR21) 2006; 110 CR17 Lambert (CR10) 1991 Ramos (CR16) 2007; 189 Jain (CR9) 1984 Burghardt, Zaleski (CR3) 1968; 23 Benzinger, Becker, Httinger (CR2) 1996; 34 Farrell (CR7) 1987; 13 Rao, Wolf, Arkin (CR19) 2002; 420 Miller (CR13) 1986; 12 Watts (CR26) 1983; 9 Calvo, Montijano, Randez (CR4) 1993; 4 Miller, O’Riordan, Shishkin (CR14) 1996 Vigo-Aguiar, Natesan (CR25) 2004; 27 Doolan, Miller, Schildres (CR6) 1980 Ramos, Vigo-Aguiar (CR18) 2008; 85 Hairer, Norsett, Wanner (CR8) 1987 CR22 Liu, Shen (CR11) 2008; 38 Liu (CR12) 2008; 320 Shampine, Witt (CR24) 1995; 62 O’Malley (CR15) 1974 Reilly, O’Riordan (CR20) 2005; 182 Aris (CR1) 1968; 24 Shampine, Gordon (CR23) 1975 Y. Liu (9636_CR12) 2008; 320 M. Calvo (9636_CR4) 1993; 4 E.P. Doolan (9636_CR6) 1980 W. Benzinger (9636_CR2) 1996; 34 C.V. Rao (9636_CR19) 2002; 420 9636_CR22 R. Aris (9636_CR1) 1968; 24 L.F. Shampine (9636_CR23) 1975 J.D. Lambert (9636_CR10) 1991 A. Burghardt (9636_CR3) 1968; 23 L.F. Shampine (9636_CR24) 1995; 62 H.A. Watts (9636_CR26) 1983; 9 J. Vigo-Aguiar (9636_CR25) 2004; 27 J.J.H. Miller (9636_CR13) 1986; 12 9636_CR17 P.A. Farrell (9636_CR7) 1987; 13 Y. Liu (9636_CR11) 2008; 38 H. Ramos (9636_CR16) 2007; 189 R.E. O’Malley (9636_CR15) 1974 M.K. Jain (9636_CR9) 1984 H. Ramos (9636_CR18) 2008; 85 M. Danish (9636_CR5) 2008; 32 M.J.O. Reilly (9636_CR20) 2005; 182 J.J.H. Miller (9636_CR14) 1996 W. Rudzinski (9636_CR21) 2006; 110 E. Hairer (9636_CR8) 1987 |
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| SubjectTerms | Chemistry Chemistry and Materials Science Exact sciences and technology General and physical chemistry Math. Applications in Chemistry Mathematical analysis Mathematics Numerical analysis Numerical analysis. Scientific computation Original Paper Partial differential equations Partial differential equations, initial value problems and time-dependant initial-boundary value problems Physical Chemistry Sciences and techniques of general use Theoretical and Computational Chemistry Theory of reactions, general kinetics. Catalysis. Nomenclature, chemical documentation, computer chemistry |
| Title | Numerical solution of nonlinear singularly perturbed problems by using a non-standard algorithm on variable stepsize implementation (CMMSE–2009) |
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