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一类奇异方程两点边值问题的差分—样条校正解 被引量:1

CORRECT SOLUTION OF THE FINITE DIFFERENCE AND THE SPLINE FUNCTION FOR A CLASS OF SINGULAR TWO-POINT BOUNDARY VALUE PROBLEMS
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摘要 本文考虑一类奇异方程两点边值问题的差分解和样条数值解法,证明了差分解,样条解分别从两侧逼近精确解,从而得到高精度的差分-样条校正解. 考虑如下形式的奇异边值问题: In this paper, numerical methods of the finite difference and the spline function fora class of singular two-point boundary value problems are considered. One-sided approxima-tion by these methods is found. So, correct solution of high order accuracy for a class of singu-lar two-point boundary value problems is obtained. Some numerical examples are given in il-lustration of this theory
作者 韩国强
出处 《计算数学》 CSCD 北大核心 1991年第2期187-192,共6页 Mathematica Numerica Sinica
基金 中山大学科研基金
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参考文献3

  • 1韩国强,计算数学,1988年,10卷,18页
  • 2黄友谦,中山大学学报,1983年,1期,50页
  • 3韩国强

同被引文献8

  • 1CHAWLA M M, KATFI C P. Finite difference methods and their con-vergence for a class of singular two point boundary value problems [J]. Numerische Mathematik, 1982,39: 341-350.
  • 2HAN W M. Asymptotic error expansions for numerical solutions of one- dimensional problems with singularities[J]. Mathematical and Computer Modeling, 1991,15(12) : 67-76.
  • 3SINGH R,KUMAR J. Solving a class of singular two point boundary value problems using new modified decomposition method[J]. ISRN Computational Mathematics,2013,23(3) : 1-11.
  • 4SINGH R, KUMAR J. An efficient numerical technique for the solution of nonlinear singular boundary value problems[J]. Computer Physics Communications,2014, 185(4) : 1282-1289.
  • 5STAKGOLD I. Green' s function and boundary value problems[M]. New York : John Wiley and Sons, 2011.
  • 6CEN Z D. Numerical study for a class of singular two-point boundary value problems using Green's functions[J]. Applied Mathematics and Computation,2006,183(5) : 10-16.
  • 7WANG T K, LI N, Gao G H. The asymptotic expansion and extrapola- tion of trapezoidal rule for integrals with fractional order singularities[J]. Interuational Journal of Computer Mathematics, 2015,92 ( 3 ) : 579-590.
  • 8PHILIP J D,PHILIP R. Methods of numerical integration[M]. 2nd. ed. San Diego: Academic Press, 1984.

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