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Continuous finite difference approximations for solving differential equations. (English) Zbl 0940.65077

The authors report continuous finite difference formulae to treat numerically both initial and boundary value problems for ordinary differential equations, without implementing shooting procedures for the latter. Error estimates are derived and computed results illustrate the feasibility of the methods proposed.

MSC:

65L10 Numerical solution of boundary value problems involving ordinary differential equations
65L12 Finite difference and finite volume methods for ordinary differential equations
65L70 Error bounds for numerical methods for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
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[1] Keller H. B., Regional Conference Series in Applied Mathematics 24 (1976)
[2] DOI: 10.1137/0714006 · Zbl 0358.65069
[3] Ascher U., Codes for Boundary Value Problems in Ordinary Differential Equations 76 (1979)
[4] DOI: 10.1090/S0025-5718-1991-1068809-4
[5] Onumanyi P., J. Nig. Math. Soc. 13 pp 37– (1994)
[6] DOI: 10.1090/S0025-5718-1989-0971403-5
[7] Jennings A., Matrix Computation for Engineers and Scientists (1977) · Zbl 0355.65018
[8] Fox, L. 1980.Numerical Methods for Boundary Value Problems in Computational Techniques for Ordinary Differential Equations, Edited by: Gladwell, I. and Sayers, D. K. 175–216. Academic Press.
[9] Jator S. N. Ph. D. Thesis in preparation University of Ilorin Ilorin Nigeria 1997 to appear
[10] DOI: 10.1137/0722068 · Zbl 0608.65044
[11] DOI: 10.1016/0898-1221(90)90072-R · Zbl 0702.65069
[12] DOI: 10.1137/0725013 · Zbl 0639.65049
[13] Awoyemi D. O. On some continuous Linear multistep methods for initial value problems Doctoral Thesis (unpublished), University of Ilorin Nigeria 1992
[14] Sirisena U. W. Ph. D. Thesis in preparation Nigeria1997 to appear
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