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Projection and multi-projection methods for second kind Volterra-Hammerstein integral equation | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 21، دوره 12، شماره 2، بهمن 2021، صفحه 275-291 اصل مقاله (429.23 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2020.18624.2026 | ||
| نویسندگان | ||
| Moumita Mandal* 1؛ Kapil Kant2؛ Gnaneshwar Nelakanti2 | ||
| 1Assistant Professor, Department of Mathematics, Indian Institute of Technology Jodhpur, Rajasthan-342037, India. | ||
| 2Department of Mathematics Indian Institute of Technology Kharagpur, Kharagpur - 721 302, India | ||
| تاریخ دریافت: 17 شهریور 1398، تاریخ پذیرش: 25 فروردین 1399 | ||
| چکیده | ||
| In this article, we discuss the piecewise polynomial based Galerkin method to approximate the solutions of second kind Volterra-Hammerstein integral equations. We discuss the convergence of the approximate solutions to the exact solutions and obtain the orders of convergence $\mathcal O(h^{r})$ and $\mathcal O(h^{2r}),$ respectively, for Galerkin and its iterated Galerkin methods in uniform norm, where $h, ~r$ denotes the norm of the partition and smoothness of the kernel, respectively. We also obtain the superconvergence results for multi-Galerkin and iterated multi-Galerkin methods. We show that iterated multi-Galerkin method has the order of convergence $\mathcal O(h^{3r})$ in the uniform norm. Numerical results are provided to demonstrate the theoretical results. | ||
| کلیدواژه‌ها | ||
| Volterra-Hammerstein integral equations؛ Galerkin method؛ Multi-Galerkin method؛ Piecewise polynomials؛ Superconvergence rates | ||
| مراجع | ||
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