TY  - JOUR
A1  - Gathungu, Duncan Kioi
A1  - Borzì, Alfio
T1  - Multigrid Solution of an Elliptic Fredholm Partial Integro-Differential Equation with a Hilbert-Schmidt Integral Operator
JF  - Applied Mathematics
N2  - An efficient multigrid finite-differences scheme for solving elliptic Fredholm partial integro-differential equations (PIDE) is discussed. This scheme combines a second-order accurate finite difference discretization of the PIDE problem with a multigrid scheme that includes a fast multilevel integration of the Fredholm operator allowing the fast solution of the PIDE problem. Theoretical estimates of second-order accuracy and results of local Fourier analysis of convergence of the proposed multigrid scheme are presented. Results of numerical experiments validate these estimates and demonstrate optimal computational complexity of the proposed framework.
KW  - elliptic problems
KW  - finite differences
KW  - fredholm operator
KW  - multigrid schemes
KW  - numerical analysis
Y1  - 2017
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-158525
VL  - 8
IS  - 7
ER  -