Mathematical Methods in Engineering pp 103-119 | Cite as
Solving the Nonlinear System of Third-Order Boundary Value Problems
Chapter
First Online:
- 516 Downloads
Abstract
We apply the reproducing kernel method to nonlinear systems of third-order boundary value problems. We have obtained meaningful results. We demonstrate these results by figures. This method is an efficient method for solving nonlinear systems.
Keywords
Third-order Boundary Value Problem Nonlinear Systems Reproducing Kernel Reproducing Kernel Method (RKM) Reproducing Kernel Hilbert Space
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
- 1.Aronszajn, N.: Theory of reproducing kernels. Trans. Am. Math. Soc. 68, 337404 (1950)MathSciNetCrossRefGoogle Scholar
- 2.Ando, T.: Reproducing kernel spaces and quadratic inequalities. T. Ando, Hokkaido University, Sapporo, vi+96pp (1987)Google Scholar
- 3.Cui, M., Lin, Y.: Nonlinear Numerical Analysis in the Reproducing Kernel Space. Nova Science Publishers Inc., New York (2009)zbMATHGoogle Scholar
- 4.Inc, M., Akgül, A.: Approximate solutions for MHD squeezing fluid flow by a novel method. Bound Value Probl. 2014, 18 (2014)Google Scholar
- 5.Akgül, A.: New reproducing kernel functions. Math. Probl. Eng. Art. ID 158134, 10pp (2015)Google Scholar
- 6.Akgül, A., Inc, M., Karatas, E., Baleanu, D.: Numerical solutions of fractional differential equations of LaneEmden type by an accurate technique. Adv. Diff. Equ. 2015, 220 (2015)Google Scholar
- 7.Akgül, A., Inc, M., Karatas, E.: Reproducing kernel functions for difference equations. Discrete Continuous Dyn. Syst. Ser. S 8(6), 1055–1064 (2015)MathSciNetCrossRefGoogle Scholar
- 8.Akgül, A., Hashemi, M.S., Inc, M., Raheem, S.A.: Constructing two powerful methods to solve the Thomas-Fermi equation. Nonlinear Dyn. https://doi.org/10.1007/s11071-016-3125-2
Copyright information
© Springer International Publishing AG, part of Springer Nature 2019