Convergence of spline collocation for Volterra integral equations

Authors:
Raul Kangro;Peeter Oja
Affiliations:
Institute of Mathematical Statistics, Tartu University, Estonia;Institute of Applied Mathematics, Tartu University, Estonia
Venue:
Applied Numerical Mathematics
Year:
2008

Citing 4
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Abstract

Estimates for step-by-step interpolation projections are established. Depending on the spectrum of the transfer matrix these estimates allow to obtain the pointwise convergence of the projectors to the identity operator or, in some limit cases, to prove stable convergence of the corresponding approximate operators of integral equations. This, via general convergence theorems for operator equations, permits to get the convergence of collocation method for Volterra integral equations of the second kind in spaces of continuous or certain times continuously differentiable functions. Applications in the case of the most practical types of splines are analyzed.