Reddy, Y. N.; Reddy, K. Anantha Numerical integration method for general singularity perturbed two point boundary value problems. (English) Zbl 1024.65061 Appl. Math. Comput. 133, No. 2-3, 351-373 (2002). Summary: A numerical integration method is presented for solving general singularly perturbed two-point boundary value problems. The original second-order differential equation is replaced by an approximate first-order differential equation with a small deviating argument. Then, the trapezoidal formula is used to obtain the three-term recurrence relationship. The proposed method is iterative on the deviating argument. To demonstrate the applicability of the method, we have solved several model linear and nonlinear examples with left-end boundary layer or right-end boundary layer or an internal layer or two boundary layers and presented the computational results. Cited in 6 Documents MSC: 65L10 Numerical solution of boundary value problems involving ordinary differential equations 34B05 Linear boundary value problems for ordinary differential equations 34B15 Nonlinear boundary value problems for ordinary differential equations 34E15 Singular perturbations for ordinary differential equations Keywords:numerical examples; singular perturbations; two point boundary value problems; boundary layer; trapezoidal formula; linear; nonlinear PDFBibTeX XMLCite \textit{Y. N. Reddy} and \textit{K. A. Reddy}, Appl. Math. Comput. 133, No. 2--3, 351--373 (2002; Zbl 1024.65061) Full Text: DOI References: [1] Angel, E.; Bellman, R., Dynamic Programming and Partial Differential Equations (1972), Academic Press: Academic Press New York · Zbl 0261.65073 [2] Bender, C. M.; Orszag, S. A., Advanced Mathematical Methods for Scientists and Engineers (1978), McGraw-Hill: McGraw-Hill New York · Zbl 0417.34001 [3] El’sgol’ts, L. E.; Norkin, S. B., Introduction to the Theory and Application of Differential Equations with Deviating Arguments (1973), Academic Press: Academic Press New York · Zbl 0287.34073 [4] (Hemker, P. W.; Miller, J. J.H., Numerical Analysis of Singular Perturbation Problems (1979), Academic Press: Academic Press New York) [5] Kadalbajoo, M. K.; Reddy, Y. N., Asymptotic and numerical analysis of singular perturbation problems: a survey, Appl. Math. Comput., 30, 223-259 (1989) · Zbl 0678.65059 [6] Kevorkian, J.; Cole, J. D., Perturbation Methods in Applied Mathematics (1981), Springer: Springer New York · Zbl 0456.34001 [7] Nayfeh, A. H., Perturbation Methods (1979), Wiley: Wiley New York · Zbl 0375.35005 [8] Nayfeh, A. H., Introduction to Perturbation Techniques (1981), Wiley: Wiley New York · Zbl 0449.34001 [9] Nayfeh, A. H., Problems in Perturbation (1985), Wiley: Wiley New York [10] O’Malley, R. E., Introduction to Singular Perturbations (1974), Academic Press: Academic Press New York · Zbl 0287.34062 [11] O’Malley, R. E., Singular Perturbation Methods for Ordinary Differential Equations (1991), Springer: Springer New York · Zbl 0743.34059 [12] Prandtl, L., (Uber flussigkeit-bewegung bei Kleiner Reibung, Verh. III. Int. Math. Kongresses (1905), Tuebner: Tuebner Leipzig), 484-491 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.