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WINTER 2013 Modified projection and the iterated modified projection methods for nonlinear integral equations
Laurence Grammont, Rekha P. Kulkarni, Paulo B. Vasconcelos
J. Integral Equations Applications 25(4): 481-516 (WINTER 2013). DOI: 10.1216/JIE-2013-25-4-481


Consider a nonlinear operator equation $ x - K ( x )=f$, where $K$ is a Urysohn integral operator with a smooth kernel. Using the orthogonal projection onto a space of discontinuous piecewise polynomials of degree $\leq r$, previous authors have established an order $r + 1$ convergence for the Galerkin solution and $2 r + 2$ for the iterated Galerkin solution. Equivalent results have also been established for the interpolatory projection at Gauss points. In this paper, a modified projection method is shown to have convergence of order $ 3 r + 3$ and one step of iteration is shown to improve the order of convergence to $ 4 r + 4$. The size of the system of equations that must be solved, in implementing this method, remains the same as for the Galerkin method.


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Laurence Grammont. Rekha P. Kulkarni. Paulo B. Vasconcelos. "Modified projection and the iterated modified projection methods for nonlinear integral equations." J. Integral Equations Applications 25 (4) 481 - 516, WINTER 2013.


Published: WINTER 2013
First available in Project Euclid: 31 January 2014

zbMATH: 1282.65170
MathSciNet: MR3161623
Digital Object Identifier: 10.1216/JIE-2013-25-4-481

Primary: 45L10 , 65J15 , 65R20

Keywords: collocation at Gauss points , Galerkin method , Urysohn integral operator

Rights: Copyright © 2013 Rocky Mountain Mathematics Consortium

Vol.25 • No. 4 • WINTER 2013
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