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Convergence of spline collocation for Volterra integral equations

Raul Kangro - No affiliation found

2008/10/01 Full-length article DOI: 10.1016/j.apnum.2007.08.004 Journal: Applied Numerical Mathematics

Abstract:

AbstractEstimates 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.