A nonasymptotic method for general linear singular perturbation problems. (English) Zbl 0618.65066
The nonasymptotic method developed by the authors [A nonasymptotic method for singular perturbation problems, ibid. (to appear)] is extended for solving general linear singularly perturbed two-point boundary-value problems. First, we discuss problems with a right-hand boundary layer. Second, we discuss problems with an interior layer. Finally, we discuss problems with two boundary layers. Numerical experience with the method for some model problems is also reported to confirm the theoretical analysis.
MSC:
| 65L10 | Numerical solution of boundary value problems involving ordinary differential equations |
| 34B05 | Linear boundary value problems for ordinary differential equations |
| 34E15 | Singular perturbations for ordinary differential equations |
Keywords:
nonasymptotic method; linear singularly perturbed two-point boundary- value problems; boundary layer; interior layerReferences:
| [1] | Kadalbajoo, M. K., andReddy, Y. N.,A Nonasymptotic Method for Singular Perturbation Problems, Journal of Optimization Theory and Applications, Vol. 55, pp. 73-84, 1987. · Zbl 0626.34065 · doi:10.1007/BF00939045 |
| [2] | Roberts, S. M.,A Boundary-Value Technique for Singular Perturbation Problems, Journal of Mathematical Analysis and Applications, Vol. 87, No. 2, 1982. · Zbl 0481.65048 |
| [3] | O’Malley, R. E.,Introduction to Singular Perturbations, Academic Press, New York, New York, 1974. |
| [4] | Kevorkian, J., andCole, J. D.,Perturbation Methods in Applied Mathematics, Springer-Verlag, New York, New York, 1981. · Zbl 0456.34001 |
| [5] | Elsgolts, L. E., andNorkin, S. B.,Introduction to the Theory and Application of Differential Equations with Deviating Arguments, Academic Press, New York, New York, 1973. |
| [6] | Angel, E., andBellman, R. E.,Dynamic Programming and Partial Differential Equations, Academic Press, New York, New York, 1972. · Zbl 0312.49011 |
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