Numerical Treatment of Nonlinear Third Order Boundary Value Problem

References

[1] A. Khan and T. Aziz, “The Numerical Solution of Third- Order Boundary-Value Problems Using Quintic Splines,” Applied Mathematics and Computation, Vol. 137, No. 2-3, 2003, pp. 253-260.
doi:10.1016/S0096-3003(02)00051-6

[2] S. Valarmathi and N. Ramanujam, “A Computational Method for Solving Boundary Value Problems for Third —Order Singularly Perturbed Ordinary Differential Equations,” Applied Mathematics and Computation, Vol. 129, No. 2-3, 2002, pp. 345-373.
doi:10.1016/S0096-3003(01)00044-3

[3] T. Y. Na, “Computational Method in Engineering Boundary Value Problems,” Academic Press, New York, 1979.

[4] N. S. Asaithambi, “A Numerical Method for the Solution of the Falkner Equation,” Applied Mathematics and Computation, Vol. 81, No. 2-3, 1997, pp. 259-264.
doi:10.1016/S0096-3003(95)00325-8

[5] X. Q. Li and M. G. Cui, “Existence and Numerical Method for Nonlinear Third-Order Boundary Value Problem in the Reproducing Kernel Space,” Boundary Value Problems, Article ID 459754, 2010, pp. 1-19.

[6] N. H. Shuaib, H. Power and S. Hibberd, “BEM Solution of Thin Film Flows on an Inclined Plane with a Bottom Outlet,” Engineering Analysis with Boundary Elements, Vol. 33, No. 3, 2009, pp. 388-398.
doi:10.1016/j.enganabound.2008.06.007

[7] A. Cabada, M. R. Grossinho and F. Minhos, “External Solutions for Third-Order Nonlinear Problems with Upper and Lower Solutions in Reversed Order,” Nonlinear Analysis: Theory, Methods and Applications, Vol. 62, 2005, pp. 1109-1121.

[8] M. Pei and S. K. Chang, “Existence and Uniqueness of Solutions for Third—Order Nonlinear Boundary Value Problems,” Journal of Mathematical Analysis and Application, Vol. 327, 2007, pp. 23-35.
doi:10.1016/j.jmaa.2006.03.057

[9] F. M. Minhos, “On Some Third Order Nonlinear Boundary Value Problems: Existence, Location and Multiplicity Results,” Journal of Mathematical Analysis and Application, Vol. 339, 2008, pp. 1342-1353.
doi:10.1016/j.jmaa.2007.08.005

[10] M. Cui and Z. Deng, “Solutions to the Definite Solutions Problem of Differential Equations in Space ,” Advances in Mathematics, Vol. 17, 1988, pp. 327-329.

[11] C. I. Li and M.-G. Cui, “The Exact Solution for Solving a Class Nonlinear Operator Equations in the Reproducing Kernel Space,” Applied Mathematics and Computation, Vol. 143, No. 2-3, 2003, pp. 393-399.
doi:10.1016/S0096-3003(02)00370-3

[12] M. Kumar and P. K. Srivastava, “Computational Techniques for Solving Differential Equations by Quadratic, Quartic and Octic Spline,” Advances in Engineering Software, Vol. 39, No. 8, 2008, pp. 646-653.
doi:10.1016/j.advengsoft.2007.09.001

[13] M. Kumar and P. K. Srivastava, “Computational Techniques for Solving Differential Equations by Cubic, Quintic and Sextic Spline,” International Journal for Computational Methods in Engineering Science & Mechanics, Vol. 10, No. 1, 2009, pp. 108-115.
doi:10.1080/15502280802623297

[14] J. Rashidinia, R. Jalilian and R. Mohammadi, “Non- Polynomial Spline Methods for the Solution of a System of Obstacle Problems,” Applied Mathematics and Computation, Vol. 188, No. 2, 2007, pp. 1984-1990.
doi:10.1016/j.amc.2006.11.074