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集值微分方程初值问题的高阶收敛性

Higher order convergence for set differential equations with initial conditions
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摘要 通过应用比较原理和拟线性方法,对所构造的单调迭代序列进行了分析,证明了其逼近解序列一致且高阶收敛于该问题的解,所得结论推广和改进了已有的研究成果. tive sequences problem were By using the comparison principle and the method of quasilinearization, two monotone itera- of approximate solutions which converge uniformly and higher order to the solution of the obtained. The results generalize and improve the known ones.
作者 王培光 刘会娜
机构地区 河北大学电子信息工程学院 河北大学数学与信息科学学院
出处 《河北大学学报（自然科学版）》 CAS 北大核心 2016年第1期1-6,共6页 Journal of Hebei University(Natural Science Edition)
基金 国家自然科学基金资助项目(11271106) 河北省自然科学基金资助项目(A2013201232)
关键词 集值微分方程 拟线性化方法 高阶收敛 set differential equations quasilinearization higher order convergence
分类号 O175.12 [理学—基础数学]
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参考文献11

  • 1BHASKAR T G, LAKSHMIKANTHAM V. Set differential equations and flow invarianee[J]. Appl Anal, 2003,82~357- 368. DOI: 10. 1080/0003681031000101529.
  • 2BHASKAR T G,LAKSHMIKANTHAM V. Lyapunov stability for set differential equations[J]. Dynam Systems Appl, 2004,13:1-10.
  • 3LAKSHMIKANTHAM V, LEE S, VATSALA A S. Set-valued hybrid dilfferential equations and stability in terms of two measures[J]. J Hybrid Syst, 2002,2 : 169-187.
  • 4LAKSHMIKANTHAM V, LEE S, VATSALA A S. Intereonneetion between set and fuzzy differential equations[J]. Noulinear Anal, 2003,54 : 351-360. DOI : 10. 1016/S0362-546X(03)00067-1.
  • 5王培光,高玮.集值微分方程初值问题的拟线性化方法[J].河北大学学报（自然科学版）,2011,31(1):1-6. 被引量：5
  • 6WANG P G,GAO W. Quasilinearization of an initial value problem for a set valued integrodifferential equation[J]. Com- puters and Mathematics with Applications,2011,61:2111-2115. DOI: 10. 1016/j. camwa. 2010.08. 084.
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  • 10王培光,侯颖,刘静.一类分数阶微分方程的广义拟线性化方法[J].河北大学学报（自然科学版）,2011,31(5):449-452. 被引量：2

二级参考文献15

  • 1TOLSTONOGOV A. Differential Inclusions in a Banach Space[M]. Dordrecht:Kluwer Academic Publishers,2000.
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  • 4LAKSMIKANTHAM V, LEELA S,VATSALA A. Interconneetion between set and fuzzy differential equations[J]. Nonlinear Anal, 2003,54 : 351-360.
  • 5RADSTROM H. An embedding theorem for space of convex sets[J]. Proc AM Math Soc, 1952,3:165-169.
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  • 7LAKSMIKANTHAM V, VATSALA A. Generalized quasilinearization for nonlinear problems[M]. Dordrecht:K|uwer Academic Publishers, 1998.
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  • 10CAPUTO M. Linear models of dissipation whose Q is almost independent Ⅱ[J]. Geophys J R Astron, 1967,13 (5) :529- 539.

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河北大学学报（自然科学版）
2016年 第1期

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