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Asymptotic error expansion of a collocation-type method for Volterra- Hammerstein integral equations. (English) Zbl 0799.65150
Consider the integral equation \(y(t)= f(t)+ \int^ t_ 0 k(t,s)g(s,y(s))ds\), \(t\in [0,T]\), or equivalently, \(z(t)= g(t,f(t)+ \int^ t_ 0 k(t,s)z(s)ds)\), \(y(t)= f(t)+ \int^ t_ 0 k(t,s)z(s)ds\), \(t\in [0,T]\). The author derives an asymptotic expansion of the collocation solution of the last equation when piecewise polynomials of \(\Pi_{p-1}\) are used. The collocation solution admits an error expansion in powers of the stepsize \(h\), beginning with term \(h^ p\), and even with \(h^{2p}\) if special collocation points are used.
Reviewer: G.Vainikko (Tartu)

65R20 Numerical methods for integral equations
45G10 Other nonlinear integral equations
45G15 Systems of nonlinear integral equations
Full Text: DOI
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