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  • 한국과학기술정보연구원(KISTI) 서울분원 대회의실(별관 3층)
  • 2024년 07월 03일(수) 13:30
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  • P-ISSN1226-0657
  • E-ISSN2287-6081
  • KCI

ISSN : 1226-0657

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Vol.21 No.1

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A NUMERICAL ALGORITHM FOR SINGULAR MULTI-POINT BVPS USING THE REPRODUCING KERNEL METHOD

A NUMERICAL ALGORITHM FOR SINGULAR MULTI-POINT BVPS USING THE REPRODUCING KERNEL METHOD

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2014, v.21 no.1, pp.51-60
https://doi.org/10.7468/jksmeb.2014.21.1.51
Jia, Yuntao (School of Science, Zhuhai Campus, Beijing Institute of Technology)
Lin, Yingzhen (School of Science, Zhuhai Campus, Beijing Institute of Technology)
Jia, Yuntao, & Lin, Yingzhen. (2014). A NUMERICAL ALGORITHM FOR SINGULAR MULTI-POINT BVPS USING THE REPRODUCING KERNEL METHOD. 한국수학교육학회지시리즈B:순수및응용수학, 21(1), 51-60, https://doi.org/10.7468/jksmeb.2014.21.1.51

Abstract

In this paper, we construct a complex reproducing kernel space for singular multi-point BVPs, and skillfully obtain reproducing kernel expressions. Then, we transform the problem into an equivalent operator equation, and give a numerical algorithm to provide the approximate solution. The uniform convergence of this algorithm is proved, and complexity analysis is done. Lastly, we show the validity and feasibility of the numerical algorithm by two numerical examples.

keywords
singular multi-point BVPs, complex reproducing kernel space, operator equation, uniform convergence

참고문헌

1.

F. Wong & W. Lian. (1996). Positice solution for singular boundary value problems. Comput. Math. Appl., 32(9), 41-49.

2.

P. Kelevedjiev. (2002). Existence of positice solution to a singular second order boundary value problem. Nonlinear Anal., 50, 1107-1118. 10.1016/S0362-546X(01)00803-3.

3.

X. Xu & J. Ma. (2004). A note on singular nonlinear boundary value problems. J. Math. Anal. Appl., 293, 108-124. 10.1016/j.jmaa.2003.12.017.

4.

Y. Liu & H. Yu. (2005). Existence and uniqueness of positice solution for singular boundary value problem. Comput. Math. Appl., 50, 133-143. 10.1016/j.camwa.2005.01.022.

5.

K. Al-Khaled. (2007). Theory and computation in singular boundary value problems. Chaos Solitons Fractals., 33, 678-684. 10.1016/j.chaos.2006.01.047.

6.

L.U. Junfeng. (2007). Variational iteration method for solving two-point boundary value problems. J. Comput. Appl. Math., 207, 92-101. 10.1016/j.cam.2006.07.014.

7.

A.S.V. Ravi Kanth & Y.N. Reddy. (2005). Cubic spline for a class of two-point boundary value problems. Appl. Math. Comput., 207, 733-740.

8.

John R. Graef & Lingju Kong. (2008). Necessary and sufficient conditions for the existence of symmetric positive solutions of multi-point boundary value problems. Nonlinear Anal., 68, 1529-1552. 10.1016/j.na.2006.12.037.

9.

Qingkai Kong & Min Wang. (2010). Positive solutions of even order system periodic boundary value problems. Nonlinear Anal., 72, 1778-1791. 10.1016/j.na.2009.09.019.

10.

Siraj-ul-Islam, Ikram A & Tirmizi. (2006). Nonpolynomial spline approach to the solution of a system of second-order boundary-value problems. Appl. Math. Comput., 173, 1208-1218. 10.1016/j.amc.2005.04.064.

11.

Siraj-ul-Islam, Imran Aziz & Booidararler. (2010). The numerical solution of second-order boundary-value problems by collocation method with the Haar wavelets. Math. Comput. Modelling., 52, 1577-1590. 10.1016/j.mcm.2010.06.023.

12.

J. Caballero, J. Harjani & K. Sadarangani. (2011). Positive solutions for a class of singular fractional boundary value problems. Comput. Math. Appl., 62, 1325-1332. 10.1016/j.camwa.2011.04.013.

13.

Tieshan He, Fengjian Yang, Chuanyong Chen & Shiguo Peng. (2011). Existence and multi-plicity of positive solutions for nonlinear boundary value problems with a parameter. Comput. Math. Appl., 61, 3355-3363. 10.1016/j.camwa.2011.04.039.

14.

Boying Wu & Yingzhen Lin. Application of the reproducing kernel space.

15.

A.S.V. Ravi Kanth & K.Aruna. (2008). Solution of singular two-point boundary value problems using differential transformation method. Phys. Lett. A., 372, 4671-4673. 10.1016/j.physleta.2008.05.019.

한국수학교육학회지시리즈B:순수및응용수학

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