一类非线性积分微分方程初值问题收敛性的进一步结果

doi:10.3969/j.issn.1000-1565.2018.05.001

河北大学学报(自然科学版) ›› 2018, Vol. 38 ›› Issue (5): 449-453.DOI: 10.3969/j.issn.1000-1565.2018.05.001

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一类非线性积分微分方程初值问题收敛性的进一步结果

王培光,杨凯愉,秦俊红

收稿日期:2018-02-23 出版日期:2018-09-25 发布日期:2018-09-25
作者简介:王培光(1963—),男,黑龙江哈尔滨人,河北大学教授,博士生导师,主要从事微分方程研究. E-mail:pgwang@hbu.edu.cn
基金资助:
国家自然科学基金资助项目(11771115);河北省高等学校科学技术研究项目(QN2017018;QN2016030);河北大学研究生创新项目(hbu2018ss46)

Further result on convergence for a class of nonlinear integro-differential equations with initial value problems

WANG Peiguang, YANG Kaiyu, QIN Junhong

College of Mathematics and Information Science, Hebei University, Baoding 071002

Received:2018-02-23 Online:2018-09-25 Published:2018-09-25

摘要/Abstract

摘要： 研究了一类非线性积分微分方程初值问题.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,证明了逼近解序列的k(k≥2)阶收敛性. 所得结论发展了已有文献的结果.

关键词: 积分微分方程, 单调迭代, 拟线性化方法, 快速收敛

Abstract: A class of nonlinear integro-differential equations with initial value problems is investigated. By using the comparison principle and the method of quasilinearization, we obtain monotone iterative sequences of approximate solutions converging to the extremal solution with rate of order k(k≥2). The result extends the known one in the literature.

Key words: integro-differential equations, monotone iterative, quasilinearization, rapid convergence

中图分类号:

O175.12

王培光,杨凯愉,秦俊红. 一类非线性积分微分方程初值问题收敛性的进一步结果[J]. 河北大学学报(自然科学版), 2018, 38(5): 449-453.

WANG Peiguang, YANG Kaiyu, QIN Junhong. Further result on convergence for a class of nonlinear integro-differential equations with initial value problems[J]. Journal of Hebei University (Natural Science Edition), 2018, 38(5): 449-453.

参考文献

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一类非线性积分微分方程初值问题收敛性的进一步结果

Further result on convergence for a class of nonlinear integro-differential equations with initial value problems

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