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Solution of fifth order boundary value problems by using local polynomial regression. (English) Zbl 1118.65347
Summary: We present a novel method based on the local polynomial regression for solving of fifth order boundary value problems. The method is tested on numerical example to demonstrate its usefulness. The method presented in this paper is also compared with those developed by S. S. Siddiqi and G. Akram [ibid. 175, No. 2, 1575–1581 (2006; Zbl 1094.65072)], as well and is observed to be better.

MSC:
65L10 Numerical solution of boundary value problems involving ordinary differential equations
34B05 Linear boundary value problems for ordinary differential equations
Citations:
Zbl 1094.65072
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References:
[1] Agarwal, R.P., Boundary value problems for high order differential equations, (1986), World Scientific Singapore · Zbl 0598.65062
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[4] N. Caglar, H. Caglar, B-Spline solution of singular boundary value problems, Appl. Math. Comput., in press, doi:10.1016/j.amc.2006.05.035. · Zbl 1107.65062
[5] Fantan, J.L.; Costa, J.; Ruso, J.M.; Preeto, G.; Sarmiento, F., A nonparametric approach to calculate critical micelle concentrations: the local polynomial regression method, Eur. phys. J. E., 13, 133-140, (2004)
[6] Siddiqi, S.S.; Twizell, E.H., Spline solutions of linear sixth-order boundary value problems, Int. J. comput. math., 60, 3, 295-304, (1996) · Zbl 1001.65523
[7] Siddiqi, S.S.; Akram, G., Solution of fifth order boundary value problems using nonpolynomial spline technique, Appl. math. comput., 175, 1575-1581, (2006) · Zbl 1094.65072
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