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has been cited by the following article:

• 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.