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Darania, Parviz, Sotoudehmaram, Fatemeh. (1404). Superconvergence and linear stability of multistep collocation method applied to Volterra integral equations with delay function θ(t). پژوهشنامه مدیریت اجرایی, 14(1), 42-61. doi: 10.22080/cjms.2021.22283.1605
Parviz Darania; Fatemeh Sotoudehmaram. "Superconvergence and linear stability of multistep collocation method applied to Volterra integral equations with delay function θ(t)". پژوهشنامه مدیریت اجرایی, 14, 1, 1404, 42-61. doi: 10.22080/cjms.2021.22283.1605
Darania, Parviz, Sotoudehmaram, Fatemeh. (1404). 'Superconvergence and linear stability of multistep collocation method applied to Volterra integral equations with delay function θ(t)', پژوهشنامه مدیریت اجرایی, 14(1), pp. 42-61. doi: 10.22080/cjms.2021.22283.1605
Darania, Parviz, Sotoudehmaram, Fatemeh. Superconvergence and linear stability of multistep collocation method applied to Volterra integral equations with delay function θ(t). پژوهشنامه مدیریت اجرایی, 1404; 14(1): 42-61. doi: 10.22080/cjms.2021.22283.1605

Superconvergence and linear stability of multistep collocation method applied to Volterra integral equations with delay function θ(t)

Caspian Journal of Mathematical Sciences
دوره 14، شماره 1 - شماره پیاپی 27، 2025، صفحه 42-61    اصل مقاله (189.44 K)
نوع مقاله: Research Articles
شناسه دیجیتال (DOI): 10.22080/cjms.2021.22283.1605
نویسندگان
Parviz Darania* ؛ Fatemeh Sotoudehmaram
Department of Mathematics, Faculty of Science, Urmia University, P.O.Box 165, Urmia-Iran
تاریخ دریافت: 21 شهریور 1400،  تاریخ بازنگری: 03 دی 1400،  تاریخ پذیرش: 08 دی 1400 
چکیده
The main purpose of this paper is to propose the superconvergence and linear stability analysis of multistep collocation method which depend on r fixed number of
previous time steps and m collocation points to solve the Volterra integral equations
of the second kind with nonlinear and non-vanishing delay. P. Darania and et al., constructed the multistep collocation method to solve a general class of nonlinear
delay integral equations including two types of linear and nonlinear lag function θ(t)
and investigated the convergence analysis of this method. This method have uniform
order m + r for any choice of collocation parameters. In this paper we shows that,
the constructed method have a high uniform order of superconvergence (2m + 2r − 1)
together with strong stability properties. Numerical examples are presented to confirm
this theoretical predictiont.
کلیدواژه‌ها
Functional equations؛ Volterra functional integral equations؛ Multistep collocation method؛ Superconvergence؛ Linear stability analysis
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