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Numerical method for a 2nth-order boundary value problem

Bo Wang|Chenmei Xu|Shuai Jian
대한수학회 (The Korean Mathematical Society)|2013.07|대한수학회지 (Journal of the KMS)|제50권 제4호|pp. 715-725

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참고문헌

키워드

finite difference schemeboundary valve problem2nth-order ordinary differential equationtotal truncation error
주제분류수학

초록

In this paper, a finite difference scheme for a two-point boun-dary value problem of 2nth-order ordinary differential equations is pre-sented. The convergence and uniqueness of the solution for the schemeare proved by means of theories on matrix eigenvalues and norm. Nu-merical examples show that our method is very simple and effective, andthat this method can be used effectively for other types of boundary valueproblems.

Abstract

In this paper, a finite difference scheme for a two-point boun-dary value problem of 2nth-order ordinary differential equations is pre-sented. The convergence and uniqueness of the solution for the schemeare proved by means of theories on matrix eigenvalues and norm. Nu-merical examples show that our method is very simple and effective, andthat this method can be used effectively for other types of boundary valueproblems.

참고문헌 (14)

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  2. M. K. Jain, "Numerical solution of a fourth-order ordinary differential equation", J. Engrg. Math, 11(4), pp.373~380 (1977)
  3. M. A. Noor, "A reliable approach for solving linear and nonlinear sixth-order boundary value problems", Int. J. Comput. Appl. Math, 2(2), pp.163~172 (2007)
  4. M. A. Noor, "Variational iteration method for solving sixth-order boundary value problems", Commun. Nonlinear Sci. Numer. Simul, 14(6), pp.2571~2580 (2009)
  5. M. H. Pei, "Existence and uniqueness of solutions to two-point boundary value problems for ordinary differential equations of order 2n", J. Systems Sci. Math. Sci, 17(2), pp.165~172 (1997)
  6. R. A. Usmani, "An O(h6) finite difference analogue for the solution of some differential equations occurring in plate deflection theory", J. Inst. Math. Appl, 20(3), pp.331~333 (1977)
  7. R. A. Usmani, "A uniqueness theorem for a boundary value problem", Proc. Amer. Math. Soc, 77(3), pp.329~335 (1979)
  8. R. A. Usmani, "Discrete methods for boundary value problems with applications in plate deflec- tion theory", Z. Angew. Math. Phys, 30(1), pp.87~99 (1979)
  9. R. A. Usmani, "Numerical solution of some ordinary differential equations occurring in plate deflection thery", J. Engrg. Math, 9(1), pp.1~10 (1975)
  10. R. A. Usmani, "Convergence of a numerical procedure for the solution of a fourth-order bound- ary value problem", Proc. Indian Acad. Sci. Sect. A Math. Sci, 88(1), pp.21~30 (1979)
  11. X. Q. Wang, "On a boundary value problem arising in elastic deflection theory", Bull. Austral. Math. Soc, 74(3), pp.337~345 (2006)
  12. A. M. Wazwaz, "The numerical solution of sixth-order boundary value problems by the modified decomposition method", Apple. Math. Comput, 118(2-3), pp.311~325 (2001)
  13. C. Xu, "Introduction to Computational Methods" (2002), Higher Education Press
  14. K. Zhang, "Algorithm and Analysis of Numerical Computation" (2003), Science Press

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