Journal of applied mathematics & informatics

한국전산응용수학회 (The Korean Society for Computational and Applied Mathematics)
권호 표지

THE ITERATION METHOD OF SOLVING A TYPE OF THREE-POINT BOUNDARY VALUE PROBLEM

  • Liu, Xiping (College of Science, University of Shanghai for Science and Technology) ;
  • Jia, Mei (College of Science, University of Shanghai for Science and Technology)
  • 발행 : 2009.05.31
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

This paper studies the iteration method of solving a type of second-order three-point boundary value problem with non-linear term f, which depends on the first order derivative. By using the upper and lower method, we obtain the sufficient conditions of the existence and uniqueness of solutions. Furthermore, the monotone iterative sequences generated by the method contribute to the minimum solution and the maximum solution. And the error estimate formula is also given under the condition of unique solution. We apply the solving process to a special boundary value problem, and the result is interesting.

키워드

참고문헌

  1. S. R. Berger, J. Chandra, Minimal and maximal solutions of non-linear boundary value problems, Pacific J. math., 71(1997),13-20.
  2. Zengji Du, Chunyan Xue, Weigao Ge, Multiple solutions for three-point boundary value problem with nonlinear terms depending on the first order derivative, Arch. Math. Vol 84 (2005) 341-349. https://doi.org/10.1007/s00013-004-1196-7
  3. Dajun Guo, Jingxian Sun, Zhaoli Liu, Functional method for nonlinear ordinary differential equation, Shandong science and technology press, Jinan, 1995 (in Chinese)
  4. Daqing Jiang, Upper and lower solutions method and a superlinear singular boundary value problem, Computers and Mathematics with Applications 44 (2002) 323-337 https://doi.org/10.1016/S0898-1221(02)00151-7
  5. Daqing Jiang, Upper and lower solutions method and a singular boundary value problem, Z. Angew. Math. Mech. 82 (2002) 7, 481-490. https://doi.org/10.1002/1521-4001(200207)82:7<481::AID-ZAMM481>3.0.CO;2-Y
  6. Rahmat Ali Khan, J. R. L. Webb, Existence of at least three solutions of a second-order three-point boundary value problem, Nonlinear Analysis, Vol 64 (2006) 1356-1366. https://doi.org/10.1016/j.na.2005.06.040
  7. Lingju Kong, Qingkai Kong, Multi-point boundary value problems of second-order differen-tial equations(I), Nonlinear Analysis. Vol 58 (2004) 909-931. https://doi.org/10.1016/j.na.2004.03.033
  8. Xu Xian, Donal O'Regan, Sun Jingxian, Multiplicity results for three-point boundary value problems with a non-well-ordered upper and lower solution condition, Mathematical and Computer Modelling 45 (2007) 189-200. https://doi.org/10.1016/j.mcm.2006.05.003
  9. Xiaojing Yang, The method of lower and upper solutions for systems of boundary value problems, Applied Mathematics and Computation 144 (2003) 169-172. https://doi.org/10.1016/S0096-3003(02)00400-9