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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)

##### MSC:
 65R20 Numerical methods for integral equations 45G10 Other nonlinear integral equations 45G15 Systems of nonlinear integral equations
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##### References:
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