Fast and accurate solvers for weakly singular integral equations

• Type: Article in International Scientific Journal
• Date: 2023-04

Authors

Grammont, L (Author) Other; Kulkarni, RP (Author) Other; vasconcelos, pb (Author) FEP

Journal

Title: Numerical Algorithms

Vol. 92 No. 4

Pages: 2045-2070

ISSN: 1017-1398

Publisher: Springer Nature

Indexing

ISI Web of Knowledge - 2 Citations

Scopus - 3 Citations

Other information

Authenticus ID: P-00X-171

DOI: 10.1007/s11075-022-01376-x

Abstract (EN): Consider an integral equation lambda u - Tu = f, where T is an integral operator, defined on C[0, 1], with a kernel having an algebraic or a logarithmic singularity. Let pi(m) 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 lambda u(m) - T pi(m)u(m) = f. As in order to achieve a desired accuracy, one may have to choose m large, we find approximations of u(m) 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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 26