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.
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.
[1] 郭大钧,孙经先. 非线性积分方程[M].济南:山东科学技术出版社,1989.
[2] LAKSHMIKANTHAM V, RAMA MOHANA RAO M. Theory of integro differential equations[M].Switzerland: Gordon and Breach Science Publishers, 1995.
[3] CORDUNEANU C. Integral equations and applications[M]. Cambridge:Cambridge University Press, 1991.
[4] 张石生. 关于一类随机积分微分方程解的存在性定理[J].四川大学学报(自然科学版),1984(1):1-8.
[5] SUN J X, ZHAO Z Q. Extremal solutions of initial value problem for integro-differential equations of mixed type in Banach spaces[J]. Ann Diff Eqs, 1992(8): 469-475.
[6] WANG G T, ZHANG L H, SONG G X. Integral boundary value problems for first order integro-differential equations with deviating arguments[J]. J Comput Appl Math, 2009(225): 602-611. DOI:10.1016/j.cam.2008.08.030.
[7] KHOSROW MALEKNEJAD, IRAJ NAJAFI KHALILSARAYE, MAHDIEH ALIZADEH. On the solution of the integro-differential equation with an integral boundary condition[J]. Numer Algor, 2014(65): 355-374. DOI: 10.1007/s11075-013-9709-8.
[8] LIU Z H, LIANG J T. A class of boundary value problems for first-order impulsive integro-differential equations with deviating arguments[J]. Journal of Computational and Applied Mathematics, 2013(237): 477-486. DOI:10.1016/j.cam.2012.06.018.
[9] LAKSHMIKANTHAM V, VATSALA A S. Generalized quasilinearization for nonlinear problems[M]. Dordrecht: Kluwer Academic Publishers, 1998.
[10] BASHIR AHMAD. A quasilinearization method for a class of integro-differential equations with mixed nonlinearities[J]. Nonlinear Anal Real Wolrd Appl, 2006(7): 997-1004. DOI: 10.1016/j.nonrwa.2005.09.003.
[11] DEO S G, LAKSHMIKANTHAM V. Method of variation of parameters for dynamic systems[M].New York:Gordon and Breach Science Publishers, 1998.
