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Fast and accurate solvers for weakly singular integral equations
Journal
Numerical Algorithms
ISSN
10171398
Date Issued
2023-04-01
Author(s)
Grammont, Laurence
Kulkarni, Rekha P.
Vasconcelos, Paulo B.
Abstract
Consider an integral equation λu-Tu=f, where T is an integral operator, defined on C[0, 1], with a kernel having an algebraic or a logarithmic singularity. Let πm denote an interpolatory projection onto a space of piecewise polynomials of degree ≤ r- 1 with respect to a graded partition of [0, 1] consisting of m subintervals. In the product integration method, an approximate solution is obtained by solving λum-Tπmum=f. As in order to achieve a desired accuracy, one may have to choose m large, we find approximations of um using a discrete modified projection method and its iterative version. We define a two-grid iteration scheme based on this method and show that it needs less number of iterates than the two-grid iteration scheme associated with the discrete collocation method. Numerical results are given which validate the theoretical results.
Volume
92
Publication link
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