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Two‐Grid Solution of Symm's Integral Equation
Author(s) -
Saranen J.,
Vainikko G.
Publication year - 1996
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19961770115
Subject(s) - mathematics , quadrature (astronomy) , discretization , grid , convergence (economics) , integral equation , collocation method , collocation (remote sensing) , nyström method , order (exchange) , mathematical analysis , differential equation , computer science , geometry , ordinary differential equation , machine learning , economic growth , electrical engineering , economics , engineering , finance
We propose two‐grid iteration methods for Symm's integral equation discretized by quadrature‐collocation or quadrature methods. Asymptotically the optimal order of error estimate is achieved already on the first iteration, for some modifications on the second iteration. This enables us to introduce some solvers which are of the optimal convergence order and cheap in a practical implementation; the cost varies between O ( N 2 ) and O ( N log N ) arithmetic operations. Numerical experiments confirm the approximation properties of the schemes.