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具有积分边界条件的常微分方程边值问题的数值解 被引量：1

Numerical Solution of the Singularly Perturbed Problem with Integral Boundary Condition
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摘要 讨论了一类具有积分边界条件的二阶常微分方程非局部边值问题的数值解.对非局部积分边界条件采用了离散的多点边值问题进行逼近,通过常系数情况下解的局部性质,建立了这类边值问题的指数型差分格式,并且给出了格式的误差分析,证明了格式是一致收敛的. This paper discusses the numerical solution of second order differential equation with integral boundary conditions. The integral boundary conditions are proved by multipoint boundary value problem. By discussing the local properties of the solution to the corresponding problem with constant coefficient, ference scheme. The error estimate is calculated, convergent. we present a exponential fitted finite difwhich shows that this method is uniformly
作者 廉海荣 王玉鹏 赵琳琳 褚宝增
机构地区 中国地质大学(北京)数理学院
出处 《数学的实践与认识》 CSCD 北大核心 2012年第20期184-190,共7页 Mathematics in Practice and Theory
基金 中央高校基本科研业务费专项资金 国家自然科学基金(11101385)
关键词 非局部边值问题 积分边界 指数型差分格式 singular perturbation integral boundary condition exponentially fitted difference scheme
分类号 O241.8 [理学—计算数学]
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参考文献12

  • 1Cannon J R. The solution of the heat equation subject to the specification of energy[Jl. Quart Appl Math, 1963, 21: 155-160.
  • 2Chegis R Yu, Chegis R Yu. Numerical solution of a heat conduction p roblem with an integral boundary condition [J]. L itovsk Mat Sb, 1984, 24:209 - 215.
  • 3Ionkin N I. Solution of a boundary value problem in heat conduction theorywith nonlocal boundary conditions[J]. Differential Equations, 1977, 13:294 - 304.
  • 4Ahmad B, Alsaedi A, Alghamdi B S. Analytic approximation of solutions of the forced Dufling e2 quation with integral boundary conditions [J]. Nonlinear Anal, 2008, 9: 1727-1740.
  • 5Benchohra M, Hamani S, Nieto J J. The method of upper and lower solutions for second order dif2 ferential inclusions with integral boundary conditions[J]. Rocky Mountain J Math, 2010, 40: 13-26.
  • 6Boucherif A. Second-order boundary value problems with integral boundary conditions[J]. Nonlinear Anal, 2009, 70: 364-371.
  • 7Cakir M, Amiraliyev G M, A finite difference method for the singularly perturbed problem with nonlocal boundary condition, Appl. Math. compu. 2005, 160: 539-549.
  • 8Feng M, Ji D, Ge W. Positive solutions for a class of boundary value problem with integral boundary conditions in Banach spaces[J]. J Comput App 1 Math, 2008, 222:351 - 363.
  • 9徐杰,么焕民.带有积分边界条件的微分方程的数值求解算法[J].哈尔滨师范大学自然科学学报,2010,26(1):33-36. 被引量：1
  • 10牟宗泽,龙永兴,彭点云,缪敬,黄林.常微分方程边值问题的局部精确数值方法[J].计算物理,2000,17(5):565-572. 被引量：3

二级参考文献16

  • 1P.Shi,Weak solution to evolution problem with a nonlocal constraint,SIAM J.Anal.,1993,24:46-58.
  • 2A.Bouziani,N.E.Benouar,Mixed problem with integral conditions for a third order parabolic equation,Kobe J.Math.,1998,15:47-58.
  • 3M.Cakir,G.M.Amiraliyer,A finite difference method for the singularly perturbed problem with nonlocal boundary condition,Appl.Math.Comput.,2005,160:539 -549.
  • 4M.Renche,A.L.Marhoune,Mixed problem with integral conditions fora high order mixed type partial differential equation,J.Appl.Math.Stoch.Anal.,2003,16:69-79.
  • 5N.Borovykh,Stability in the numerical solution of the heat e-quation with nonlocal boundary conditions,Appl.Numer.Math.,2002,42:17-27.
  • 6W.Jiang,M.G.Cui,The exact solution and stability analysis for integral equation ofthird or first kind with singular kernel,Appl.Math.Comput.,2008,202:667 -674.
  • 7B.Ahmad,B.Alghamdi,Extended versions of quasirineariza tion for the forced Duffing equation,Comm.Appl.Nonlinear Anal.,2007,4(14):67-75.
  • 8C.L.Tang,Solvability of the forced Duffing equation at resonance,J.Math.Anal.Appl.,1998,219:110-124.
  • 9D.Jiang,J.J.Nieto,W.Zuo,On monotone method for first order and second periodic boundary value problems and periodic solutions of functional differential equation,J.Math.Anal.Appl.,2004,289:691-699.
  • 10B.Ahmad,Analytic approximation of solutions of the forced Duffing equation with integral boundary conditions,Nonlinear Anal.:Real World Appl.,2008,9:1727-1740.

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数学的实践与认识
2012年 第20期

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