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On discrete superconvergence properties of spline collocation methods for nonlinear Volterra integral equations. (English) Zbl 0758.65083

It is shown that the error corresponding to certain spline collocation approximations for nonlinear Volterra integral equations of the second kind is the solution of a nonlinearly perturbed linear Volterra integral equation.
On the basis of this result it is possible to derive general estimates for the order of convergence of the spline solution at the underlying mesh points. Extensions of these techniques to other types of Volterra equations are indicated.

MSC:

65R20 Numerical methods for integral equations
45G10 Other nonlinear integral equations
45D05 Volterra integral equations
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