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Superconvergence of interpolated collocation solutions for Hammerstein equations
Author(s) -
Huang Qiumei,
Zhang Shuhua
Publication year - 2010
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20429
Subject(s) - superconvergence , collocation (remote sensing) , interpolation (computer graphics) , mathematics , orthogonal collocation , collocation method , iterated function , convergence (economics) , partial differential equation , partial derivative , mathematical analysis , differential equation , finite element method , computer science , ordinary differential equation , animation , physics , computer graphics (images) , machine learning , economic growth , economics , thermodynamics
In this article, we discuss the superconvergence of the interpolated collocation solutions for Hammerstein equations. Applying this new interpolation postprocessing to the collocation approximation x h , we get a higher accuracy approximation I 2 h 2 r ‐1x h , whose convergence order is the same as that of the iterated collocation method. Such an interpolation postprocessing method is much simpler. Also, numerical experiments are shown to demonstrate the efficiency of the interpolation postprocessing method. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010