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求解一类四阶奇异边值问题的新算法

Solving Singular Boundary-value Problem of Fourth Order in the Reproducing Kernel Space
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摘要 在再生核空间W5[0,1]中求解一类四阶奇异边值,给出精确解的级数形式的精确表达式.证明近似解一致收敛于精确解.数值算例验证了算法的有效性. In this paper,a method for solving singular boundary-value problem of fourthe order in the reproducing kernel space is presented.The exact solution is represented in the form of series in the reproducing kernel space.In the mean time,the n_term approximate solution is proved to converge to the exact solution.The high precision of this method is demonstrated by the numerical examples.
作者 贺裕 么焕民
机构地区 哈尔滨师范大学
出处 《哈尔滨师范大学自然科学学报》 CAS 2010年第1期13-17,共5页 Natural Science Journal of Harbin Normal University
基金 黑龙江省自然科学基金(A2007-11) 黑龙江省教育厅骨干教师计划项目(1151G09) 哈尔滨师范大学博士启动基金项目资助(KGB200901)
关键词 精确解 奇异两点边值问题 再生核空间 Exact solution Singular boundary value problem Reproducing kernel
分类号 O175.8 [理学—基础数学]
  • 相关文献

参考文献9

  • 1D.O'Regan.Solvability of some fourth (and higher) order singular boundary value problems.J.Math.Anal.Appl.,1991,161:78-116.
  • 2S.Charkrit,A.Kananthai.Existence of solutions for some higher order boundary value problems.J.Math.Anal.Appl.,2007,329:830-850.
  • 3A.M.Wazwaz.The numerical solution of special fourth-order boundary value problems by the modified decomposition method.Int.J.Comput.Math.,2002,79(3):345-356.
  • 4S.Momani,K.Moadi.A reliable algorithm for solving fourth-order boundary value problems.J.Appl.Math.Comput,2006,22(3):185-197.
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  • 6V.S.Erturk,S.Momani.Comparing numerical methods for solving fourth-order boundary value problems.Applied Math-ematics and Computation,2007,188:1963-1968.
  • 7林迎珍,么焕民.求解含有转向点的奇异扰动问题的新算法[J].哈尔滨师范大学自然科学学报,2007,23(2):24-27. 被引量：2
  • 8S.Mornani,M.A.Noor.Numerical comparison of methods for solving a special fourth-order boundary value problem.Applied Mathematics and Computation,2007,191:218-224.
  • 9M.G.Cui,Y.Z.Lin.Nonlinear numercial analysis in the reproducing kernel space.Nova Science Publisher,New York,2008.

二级参考文献6

  • 1[6]Fazhan Geng,Minggen Cui.Solving a nonlinear system of second order boundary value problems.J.Math.Anal.Appl.,2007,327:1167 ～ 1181.
  • 2[7]Chunli Li,Minggen Cui.The exact solution for solving a class nonlinear operator equations in the reproducing kernel space.Apppl.Math.Compu.,2003,143:393 ～ 399.
  • 3[1]A.M.Watts.A singular perturbation problem with a turning point.Bull.Austral.Math.Soc..1971,5:61 ～73.
  • 4[2]D.R.Smith.Singular-perturbation Theory.Cambridge University Press,Cambridge,1985.
  • 5[3]A.Wazwaz.Two Turuing Points of Second order.SIAM J.Appl.Math.,1990,50:883 ～ 892.
  • 6[4]Heping Yang.On a singular perturbation problem with two second -order turning points.Journal of Computational and Applied Mathematics,2006,190:287 ～ 303.

共引文献1

哈尔滨师范大学自然科学学报
2010年 第1期

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