Kellogg, R. Bruce; Tsan, Alice Analysis of some difference approximations for a singular perturbation problem without turning points. (English) Zbl 0418.65040 Math. Comput. 32, 1025-1039 (1978). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 4 ReviewsCited in 210 Documents MSC: 65L10 Numerical solution of boundary value problems involving ordinary differential equations 34E15 Singular perturbations for ordinary differential equations 34B05 Linear boundary value problems for ordinary differential equations Keywords:difference approximations; singular perturbation problem; two point boundary value problem; difference schemes; backward Euler PDF BibTeX XML Cite \textit{R. B. Kellogg} and \textit{A. Tsan}, Math. Comput. 32, 1025--1039 (1978; Zbl 0418.65040) Full Text: DOI OpenURL References: [1] Fred Dorr, The numerical solution of singular perturbations of boundary value problems, SIAM J. Numer. Anal. 7 (1970), 281 – 313. · Zbl 0213.16704 [2] A. M. Il\(^{\prime}\)in, A difference scheme for a differential equation with a small parameter multiplying the highest derivative, Mat. Zametki 6 (1969), 237 – 248 (Russian). [3] K. E. Barrett, The numerical solution of singular-perturbation boundary-value problems, Quart. J. Mech. Appl. Math. 27 (1974), 57 – 68. · Zbl 0285.65053 [4] L. R. Abrahamsson, H. B. Keller, and H. O. Kreiss, Difference approximations for singular perturbations of systems of ordinary differential equations, Numer. Math. 22 (1974), 367 – 391. · Zbl 0314.65042 [5] Joseph E. Flaherty and R. E. O’Malley Jr., The numerical solution of boundary value problems for stiff differential equations, Math. Comput. 31 (1977), no. 137, 66 – 93. · Zbl 0402.65049 [6] Murray H. Protter and Hans F. Weinberger, Maximum principles in differential equations, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1967. · Zbl 0549.35002 [7] Richard S. Varga, Matrix iterative analysis, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1962. · Zbl 0133.08602 [8] Philip J. Davis, Interpolation and approximation, Blaisdell Publishing Co. Ginn and Co. New York-Toronto-London, 1963. [9] V. A. GUSHCHIN &. V. V. SHCHENNIKOV, ”A monotonic difference scheme of secondorder accuracy,” U.S.S.R. Computational Math. and Math. Phys., v. 14, 1974, pp. 252-256. 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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.