Reddy, Y. N.; Pramod Chakravarthy, P. An initial-value approach for solving singularly perturbed two-point boundary value problems. (English) Zbl 1058.65079 Appl. Math. Comput. 155, No. 1, 95-110 (2004). Summary: An initial-value approach is presented for solving singularly perturbed two-point boundary value problems with the boundary layer at one end (left or right) point. This approach is based on the boundary layer behavior of the solution. The method is distinguished by the following fact: The given singularly perturbed two-point boundary value problem is replaced by three first order initial-value problems. Several linear and non-linear problems are solved to demonstrate the applicability of the method. It is observed that the present method approximates the exact solution very well. Cited in 26 Documents MSC: 65L10 Numerical solution of boundary value problems involving ordinary differential equations 35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs 34B15 Nonlinear boundary value problems for ordinary differential equations 34E15 Singular perturbations for ordinary differential equations Keywords:singular perturbation; numerical examples; initial-value method; two-point boundary value problems; boundary layer; linear and non-linear problems PDFBibTeX XMLCite \textit{Y. N. Reddy} and \textit{P. Pramod Chakravarthy}, Appl. Math. Comput. 155, No. 1, 95--110 (2004; Zbl 1058.65079) Full Text: DOI References: [1] Bender, C. M.; Orszag, S. A., Advanced Mathematical Methods for Scientists and Engineers (1978), McGraw-Hill: McGraw-Hill New York · Zbl 0417.34001 [2] Kadalbajoo, M. K.; Reddy, Y. N., Initial-value technique for a class of nonlinear singular perturbation problems, Journal of Optimization Theory and Applications, 53, 395-406 (1987) · Zbl 0594.34017 [3] Kevorkian, J.; Cole, J. D., Perturbation Methods in Applied Mathematics (1981), Springer-Verlag: Springer-Verlag New York · Zbl 0456.34001 [4] Nayfeh, A. H., Perturbation Methods (1973), Wiley: Wiley New York · Zbl 0375.35005 [5] O’Malley, R. E., Introduction to Singular Perturbations (1974), Academic Press: Academic Press New York · Zbl 0287.34062 [6] Reinhardt, H. J., Singular perturbations of difference methods for linear ordinary differential equations, Applicable Analysis, 10, 53-70 (1980) [7] Roberts, S. M., A boundary-value technique for singular perturbation problems, Journal of Mathematical Analysis and Applications, 87, 489-503 (1982) · Zbl 0481.65048 [8] Roberts, S. M., The analytical and approximate solutions of \(εy^{′′} = yy^′\), Journal of Mathematical Analysis and Applications, 97, 245-265 (1983) · Zbl 0523.34003 [9] Roberts, S. M., Solution of \(εy^{′′} + yy^′\)−\(y=0\) by a non asymptotic method, Journal of Optimization Theory and Applications, 44, 303-332 (1984) · Zbl 0534.34062 [10] Smith, D. R., Singular-Perturbation Theory an Introduction with Applications (1985), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0567.34055 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.