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On spline approximation for a class of integral equations. I: Galerkin and collocation methods with piecewise polynomials
Author(s) -
Elschner Johannes
Publication year - 1988
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670100505
Subject(s) - mathematics , piecewise , superconvergence , galerkin method , collocation method , iterated function , norm (philosophy) , basis function , collocation (remote sensing) , orthogonal collocation , mathematical analysis , spline (mechanical) , integral equation , class (philosophy) , finite element method , differential equation , ordinary differential equation , physics , remote sensing , structural engineering , engineering , geology , political science , law , thermodynamics , artificial intelligence , computer science
We consider the numerical solution of a class of one‐dimensional non‐compact integral equations by Galerkin and collocation methods and their iterated variants, using piecewise polynomials as basis functions. In particular, we obtain new results for the stability of the approximation methods, without any restriction on the norm of the integral operators. Furthermore, we extend results of Chandler and Graham 4,6 concerning error estimates and superconvergence to a more general class of operators.