TITLE:
Multigrid Solution of an Elliptic Fredholm Partial Integro-Differential Equation with a Hilbert-Schmidt Integral Operator
AUTHORS:
Duncan Kioi Gathungu, Alfio Borzì
KEYWORDS:
Elliptic Problems, Fredholm Operator, Multigrid Schemes, Finite Differences, Numerical Analysis
JOURNAL NAME:
Applied Mathematics,
Vol.8 No.7,
July
18,
2017
ABSTRACT: 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.