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Faraidun K. Hama-Salh, Dhuha M. Salih
School of Science Education, University of Sulaimani
DOI: https://doi.org/10.17656/jzs.10237
Abstract:
In this paper, we derive some difference schemes for the initial value problems using
approximate spline interpolation, with the sixth degree lacunary spline function that
interpolates the solution function of the problem; first and fourth order accurate schemes
are obtained. To test the efficiency of the method, several numerical examples of third and
fifth order initial value problems are solved by proposed method.
Keywords: Differential equations, Spline interpolation, Absolute error, Lipchitz condition.
References
1-Faraga, R. (Ed.), “Calculus Problems for a New Century”, Mathematical Association of America (MAA Notes Number 28), Washington, D.C. (1993).
2-Gyovari, J. “Spline function and the Cauchy problem”, Constructive Theory of Functions, 81: pp. 344-348, (1984).
3-Gyovari, J. “Cauchy problem and modified lacunary spline functions”, Constructive Theory of Functions, 84: pp. 392-396, (1984).
4-Jwamer, K.J. and Kareem, R.G. “Lacunary spline solution of fourth order initial value problem”, Asian Journal of Mathematics and Statistics, 3(3):119-129, (2010).
5-Karwan H-F Jwamer, Faraidun K. Hamasalh “On Optimality of Lacunary Interpolation for Recovery of C6 Seventh Degree Spline”, Int. J. Open Problem Compt. Math., Vol. 5, No. 1, 103-113, (2012).
6-Kells, L.M. “Elementary Differential Equations”, 6th Edition, McGraw Hill; ISBN 07-033530-3, (1960).
7-Meir, A. and Sharma, A. “Lacunary interpolation by splines”, SIAM J. Numer. Anal., 10(3), pp. 433-442, (1973).
8-Rostam Saeed, Faraidun K. Hamasalh, Gulnar W. Sadiq, “Convergence of Ninth Spline Function to the Solution of a System of Initial Value Problems”, World Applied Science Journal, 16 (10), pp.1360-1367,(2012).
9-Saeed, R.K. “The solution of Cauchy's problem by using six degree spline”, J. Dohuk Univ., 3(1), pp. 22-25, (2000).
10-Saxena, A. “Solution of Cauchy's Problem by Deficient Lacunary Spline Interpolations”, Studia Univ. Babes-Bolyai Mathematica, 32, pp.60- 70, (1987).
11-Yang, W.Y., Cao, W.w. and Tae, S. “Applied Numerical Methods using Matlab”, Chung and John Morris (Eds.), John Wiley and Son, Inc., New Jersey, Published in Canada, (2005).
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