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Vemuri, V.; Raefsky, A.

On a method of solving sensitive boundary value problems. (English) Zbl 0401.65052

J. Franklin Inst. 307, 217-243 (1979).
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Cited in 5 Documents

MSC:

65L10 Numerical solution of boundary value problems involving ordinary differential equations
34D15 Singular perturbations of ordinary differential equations

Keywords:

Nonlinear Two-Point Boundary Value Problems; Sensitive Boundary Value Problems; Ordinary Differential Equations; Multi-Point Quasilinearization; Troesch’s Problem; Singular Perturbation Problem; Numerical Method
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References:

[1] Troesch, B. A., (Lecture Notes in Mathematics (1974), Springer: Springer New York, NY), 408-433, No. 362
[2] Troesch, B. A., Intrinsic difficulties in the numerical solution of a boundary value-problem, TRW (1960), Redondo Beach, California · Zbl 0117.19604
[3] Troesch, B. A., A simple approach to a sensitive two-point boundary value problem, J. Comput. Phys., Vol. 21, 279-290 (1976) · Zbl 0334.65063
[4] Roberts, S. M.; Shipman, J. S., Solutions of Troesch’s two-point boundary value problem by a combination of techniques, J. Comput. Phys., Vol. 10, 232-241 (1972) · Zbl 0247.65052
[5] Roberts, S. M.; Shipman, J. S., On the closed form solution of Troesch’s problem, J. Comput. Phys., Vol. 21, 291-304 (1976) · Zbl 0334.65062
[6] O’Malley, R. E., Introduction to Singular Perturbations (1974), Academic Press: Academic Press New York · Zbl 0287.34062
[7] Bellman, R. E.; Kalaba, R. E., Quasilinearization and Nonlinear Boundary Value Problems (1965), American Elsevier: American Elsevier New York, NY · Zbl 0139.10702
[8] Miele, A.; Iyer, R. R., Modified quasilinearization method for solving nonlinear, two-point boundary-value problems, J. math. Analysis Applic., Vol. 36, 674-692 (1971) · Zbl 0226.65058
[9] Keller, H. B., Numerical Methods for Two-Point Boundary Value Problems (1968), Blaisdell, Waltham, MA · Zbl 0172.19503
[10] Csendes, Z.; Gopinath, A.; Silvester, P., Generalized matrix inverse techniques for local approximations to operator equations, (Whiteman, J. R., The Mathematics of Finite Elements and Applications (1975), Academic Press: Academic Press London), 189-199 · Zbl 0279.65093
[11] Raefsky, A.; Vemuri, V., A numerical method for boundary value problems, Int. J. Computers Elect. Engng., Vol. 5, 85-104 (1978) · Zbl 0377.65039
[12] Eisemann, K., A heuristic description of generalized inversion, IEEE Trans. Circuit Theory, Vol. 20, No. 5, 481-487 (1973)
[13] Miele, A.; Well, K. H.; Tietze, J. L., Multipoint approach to the two-point boundary value problem, J. math. Analysis Applic., Vol. 44, No. 3, 625-642 (1973) · Zbl 0266.34020
[14] Miele, A.; Aggarwal, A. K.; Tietze, J. L., Solution of two-point boundary-value problems with Jacobian matrix characterized by large positive eigenvalues, J. Comput. Phys., Vol. 15, No. 2, 117-133 (June 1974) · Zbl 0303.65075
[15] Miele, A.; Well, K. H.; Iyer, R. R., General technique for solving nonlinear two-point boundary value problems via the methods of particular solutions, J. Optim. Theory Applic., Vol. 5, 382-399 (1970) · Zbl 0184.19905
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