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On Continuous Approximate Solution of Ordinary Differential Equations
De Ting Wu
Pages - 28 - 46     |    Revised - 15-05-2012     |    Published - 20-06-2012
Volume - 3   Issue - 1    |    Publication Date - June 2012  Table of Contents
Continuous approximate solution, Discrete approximate solution, Cubic spline interpolant
In this work the problem of continuous approximate solution of the ordinary differential equations will be investigated. An approach to construct the continuous approximate solution, which is based on the discrete approximate solution and the spline interpolation, will be provided. The existence and uniqueness of such continuous approximate solution will be pointed out. Its error will be estimated and its convergence will be considered. Finally, with the aid of modern PC and nathematical software three practical computer approaches to perform above construction will be offered.
1 Google Scholar 
2 CiteSeerX 
3 refSeek 
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Birhoff, Garrett & De Boor, Carl: "Error Bounds for Spline Interpolation", Journal of Mathematics and Mechanics, Vol 13, No 5, 1964.
Burden, Richard L & Faires, J. Douglas: "Numerical Analysis" 8th edition, Brooks/Cole, Tomson Learning Inc. 2004.
Davis,P.J.: "Interpolation and approximation", Blaisdell, New York, 1963.
De Boor, Carl:"A practical guide to spline", Spring Verlag Inc., New York, 2001.
E.Hairer, S.P.Norsett, G.W.Wanner: "Solving Ordinary Differential Equstion I" (nonstiff problem) Springer, 1993 Vol. 1
E.Hairer, S.P.Norsett, G.W.Wanner: "Solving Ordinary Differential Equstion II" (stiff and differential algebraic problem) Springer, 1996.
Loscalzo, F.R. 7 Tallot,T.D.:"Spline function approximation for solutions of ordinary differential equations", SIAM J., Numerical Analysis 4, 1967, p433 - 445.
Schoenberg, I. J: " On spline functions", In Tech Summary Rep. 625. Mathematics Research Center, University of Wisconsin, Madison, 1966.
WU, D.T.: "Mathcad's Program Function and Application in teaching of Mathmatics" in Electronic Proceeding of ICMCM 16, Aug. 2004
Wu, D.T.:"Teaching Numerical Analysis with Mathcad", The International Journal of Computer Algebra in Mathematical Edication, 10 No 1, 2003.
Dr. De Ting Wu
- United States of America