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Volume 10, Issue 4
On Discrete Superconvergence Properties of Spline Collocation Methods for Nonlinear Volterra Integral Equations

Hermann Brunner

J. Comp. Math., 10 (1992), pp. 348-357.

Published online: 1992-10

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  • Abstract

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.  

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@Article{JCM-10-348, author = {Hermann Brunner}, title = {On Discrete Superconvergence Properties of Spline Collocation Methods for Nonlinear Volterra Integral Equations}, journal = {Journal of Computational Mathematics}, year = {1992}, volume = {10}, number = {4}, pages = {348--357}, abstract = {

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.  

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9367.html} }
TY - JOUR T1 - On Discrete Superconvergence Properties of Spline Collocation Methods for Nonlinear Volterra Integral Equations AU - Hermann Brunner JO - Journal of Computational Mathematics VL - 4 SP - 348 EP - 357 PY - 1992 DA - 1992/10 SN - 10 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9367.html KW - AB -

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.  

Hermann Brunner. (1992). On Discrete Superconvergence Properties of Spline Collocation Methods for Nonlinear Volterra Integral Equations. Journal of Computational Mathematics. 10 (4). 348-357. doi:
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