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- Title
Discrete projection methods for Hammerstein integral equations on the half-line.
- Authors
Nahid, Nilofar; Nelakanti, Gnaneshwar
- Abstract
In this paper, we study discrete projection methods for solving the Hammerstein integral equations on the half-line with a smooth kernel using piecewise polynomial basis functions. We show that discrete Galerkin/discrete collocation methods converge to the exact solution with order O (n - m i n { r , d }) , whereas iterated discrete Galerkin/iterated discrete collocation methods converge to the exact solution with order O (n - m i n { 2 r , d }) , where n - 1 is the maximum norm of the graded mesh and r denotes the order of the piecewise polynomial employed and d - 1 is the degree of precision of quadrature formula. We also show that iterated discrete multi-Galerkin/iterated discrete multi-collocation methods converge to the exact solution with order O (n - m i n { 4 r , d }) . Hence by choosing sufficiently accurate numerical quadrature rule, we show that the convergence rates in discrete projection and discrete multi-projection methods are preserved. Numerical examples are given to uphold the theoretical results.
- Publication
Calcolo, 2020, Vol 57, Issue 4, p1
- ISSN
0008-0624
- Publication type
Article
- DOI
10.1007/s10092-020-00386-2