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Analysis of some difference approximations for a singular perturbation problem without turning points. (English) Zbl 0418.65040

MSC:
65L10 Numerical solution of boundary value problems involving ordinary differential equations
34E15 Singular perturbations, general theory for ordinary differential equations
34B05 Linear boundary value problems for ordinary differential equations
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[1] Fred Dorr, The numerical solution of singular perturbations of boundary value problems, SIAM J. Numer. Anal. 7 (1970), 281 – 313. · Zbl 0213.16704 · doi:10.1137/0707021 · doi.org
[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).
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[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 · doi:10.1007/BF01436920 · doi.org
[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.
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