Numerical Solutions of a Class of Second Order Boundary Value Problems on Using Bernoulli Polynomials

References

[1] M. I. Bhatti and P. Bracken, “Solutions of Differential Equations in a Bernstein Polynomial Basis,” Journal of Computational and Applied Mathematics, Vol. 205, No. 1, 2007, pp. 272-280. doi:10.1016/j.cam.2006.05.002

[2] M. A. Ramadan, I. F. Lashien and W. K. Zahra, “Polynomial and Nonpolynomial Spline Approaches to the Numerical Solution of Second Order Boundary Value Problem,” Applied Ma-thematics and Computation, Vol. 184, No. 2, 2007, pp. 476-484.
doi:10.1016/j.amc.2006.06.053.

[3]
R.A. Usmani and M. Sakai, “A Connection between Quartic Spline and Numerov Solution of a Boundary Value Problem,” International Journal of Computer Mathematics, Vol. 26, No. 3, 1989, pp. 263-273.
doi:10.1080/00207168908803700

[4]
Arshad Khan, “Parametric Cubic Spline Solution of Two Point Boundary Value Problems,” Applied Mathematics and Com-putation, Vol. 154, No. 1, 2004, pp. 175-182.
doi:10.1016/S0096-3003(03)00701-X.

[5]
E. A. Al-Said, “Cubic Spline Method for Solving Two Point Boundary Value Problems,” Korean Journal of Computational and Applied Mathematics, Vol. 5, 1998, pp. 759-770.

[6]
E. A. Al-Said, “Quadratic Spline Solution of Two Point Boun-dary Value Problems,” Journal of Natural Geometry, Vol. 12, 1997, pp. 125-134.

[7]
D. J. Fyfe, “The Use of Cubic Splines in the Solution of Two Point Boundary Value Problems,” The Computer Journal, Vol. 12, No. 2, 1969, pp. 188-192.
doi:10.1093/comjnl/12.2.188

[8]
A. K. Khalifa and J. C. Eilbeck, “Collocation with Quadratic and Cubic Splines,” The IMA Journal of Numerical Analysis, Vol. 2, No. 1, 1982, pp. 111-121.
doi:10.1093/imanum/2.1.111

[9]
G. Mullenheim, “Solving Two-Point Boundary Value Problems with Spline Functions,” The IMA Journal of Numerical Analysis, Vol. 12, No. 4, 1992, pp. 503-518.
doi:10.1093/imanum/12.4.503

[10]
J. Reinkenhof, “Differentiation and Integration Using Bernstein’s Polynomials,” International Journal for Numerical Methods in Engineering, Vol. 11, No. 10, 1977, pp. 1627-1630. doi:10.1002/nme.1620111012

[11]
E. Kreyszig, “Bernstein Polynomials and Numerical Integra-tion,” International Journal for Numerical Methods in Engi-neering, Vol. 14, No. 2, 1979, pp. 292-295.
doi:10.1002/nme.1620140213

[12]
R. A. Usmani, “Bounds for the Solution of a Second Order Differential Equation with Mixed Boundary Conditions,” Journal of Engineering Mathematics, Vol. 9, No. 2, 1975, pp. 159-164. doi:10.1007/BF01535397

[13]
B. Bialecki, “Sinc-Collocation Methods for Two Point Boundary Value Problems,” The IMA Journal of Numerical Analysis, Vol. 11, No. 3, 1991, pp. 357-375.
doi:10.1093/imanum/11.3.357

[14]
K. E. Atkinson, “An Introduction to Numerical Analysis,” 2nd Edition, John Wiley and Sons, New York, 1989, pp- 284.

[15]
P. E. Lewis and J. P. Ward, “The Finite Element Method, Prin-ciples and Applications,” Addison-Wesley, Boston 1991.

[16]
R. L. Burden and J. D. Faires, “Numerical Analysis,” Brooks/Cole Publishing Co., Pacific Grove, 1992.

[17]
M. K. Jain, “Numerical Solution of Differential Equations,” 2nd Edition, New Age International, New Delhi, 2000.