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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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آمار تعداد مشاهده مقاله: 84 تعداد دریافت فایل اصل مقاله: 9 |
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