10.1186/2251-7456-6-16

Reproducing kernel method for singular multi-point boundary value problems

HTML PDF
  • Xiuying Li*1,
  • Boying Wu2,
  1. Department of Mathematics, Changshu Institute of Technology, Changshu, Jiangsu, 215500, CN
  2. Department of Mathematics, Harbin Institute of Technology, Harbin, Heilongjiang, 150001, CN
Cover Image

Published in Issue 2012-07-20

How to Cite

Li, X., & Wu, B. (2012). Reproducing kernel method for singular multi-point boundary value problems. Mathematical Sciences, 6(1). https://doi.org/10.1186/2251-7456-6-16
Crossref
Scopus
Google Scholar
Europe PMC

HTML views: 5

PDF views: 77

Abstract

Abstract Purpose In this paper, we shall present an algorithm for solving more general singular second-order multi-point boundary value problems. Methods The algorithm is based on the quasilinearization technique and the reproducing kernel method for linear multi-point boundary value problems. Results Three numerical examples are given to demonstrate the efficiency of the present method. Conclusions Obtained results show that the present method is quite efficient.

Keywords

  • Reproducing kernel method; Singular multi-point boundary value problem; Numerical solutions
HTML PDF

References

  1. Moshiinsky (1950) Sobre los problemas de condiciones a la frontiera en una dimension de caracteristicas discontinuas (pp. 1-25)
  2. Timoshenko (1961) McGraw-Hill
  3. Agarwal and Kiguradze (2004) On multi-point boundary value problems for linear ordinary differential equations with singularities (pp. 131-151) https://doi.org/10.1016/j.jmaa.2004.05.002
  4. Du (2008) Solvability of functional differential equations with multi-point boundary value problems at resonance (pp. 2653-2661) https://doi.org/10.1016/j.camwa.2007.10.015
  5. Feng and Webb (1997) Solvability of m-point boundary value problems with nonlinear growth (pp. 467-480) https://doi.org/10.1006/jmaa.1997.5520
  6. Thompson and Tisdell (2001) Three-point boundary value problems for second-order, ordinary, differential equation (pp. 311-318) https://doi.org/10.1016/S0895-7177(01)00063-2
  7. Kwong (2006) The shooting method and multiple solutions of two/multi-point BVPs of second-order ODE (pp. 1-14)
  8. Zou et al. (2007) On the numerical studies of multi-point boundary value problem and its fold bifurcation (pp. 527-537) https://doi.org/10.1016/j.amc.2006.07.064
  9. Lin and Lin (2010) Numerical algorithm about a class of linear nonlocal boundary value problems (pp. 997-1002) https://doi.org/10.1016/j.aml.2010.04.025
  10. Tatari and Dehghan (2006) The use of the Adomian decomposition method for solving multipoint boundary value problems (pp. 672-676) https://doi.org/10.1088/0031-8949/73/6/023
  11. Yao (2005) Successive iteration and positive solution for nonlinear second-order three-point boundary value problems (pp. 433-444) https://doi.org/10.1016/j.camwa.2005.03.006
  12. Geng (2009) Solving singular second order three-point boundary value problems using reproducing kernel Hilbert space method (pp. 2095-2102) https://doi.org/10.1016/j.amc.2009.08.002
  13. Wu and Li (2010) Application of reproducing kernel method to third order three-point boundary value problems (pp. 3425-3428) https://doi.org/10.1016/j.amc.2010.09.009
  14. Li and Wu (2011) Reproducing kernel method for singular fourth order four-point boundary value problems (pp. 147-151)
  15. Tirmizi et al. (2005) A numerical method for third-order non-linear boundary-value problems in engineering (pp. 103-109) https://doi.org/10.1080/0020716042000261469
  16. Cui and Lin (2009) Nova Science Pub Inc
  17. Cui and Geng (2007) Solving singular two-point boundary value problem in reproducing kernel space (pp. 6-15) https://doi.org/10.1016/j.cam.2006.04.037
  18. Geng and Cui (2007) Solving singular nonlinear second-order periodic boundary value problems in the reproducing kernel space (pp. 389-398) https://doi.org/10.1016/j.amc.2007.03.016
  19. Geng and Cui (2012) A reproducing kernel method for solving nonlocal fractional boundary value problems (pp. 818-823) https://doi.org/10.1016/j.aml.2011.10.025
  20. Geng (2011) A novel method for solving a class of singularly perturbed boundary value problems based on reproducing kernel method (pp. 4211-4215) https://doi.org/10.1016/j.amc.2011.09.052
  21. Mohammadi and Mokhtari (2011) Solving the generalized regularized long wave equation on the basis of a reproducing kernel space (pp. 4003-4014) https://doi.org/10.1016/j.cam.2011.02.012