Spline function approximations to the solution of singular Volterra integral equations of the second kind

An arbitrarily high-order method for the approximate solution of singular Volterra integral equations of the second kind is presented. The approximate solution is a spline function of degree m, deficiency (m-1), i.e. in the continuity class C, and the method is of order m+1. For m=2 and 3 the method...

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Detalles Bibliográficos
Autor principal: El-Tom, M E A
Lenguaje:eng
Publicado: 1974
Materias:
Engineering
Acceso en línea:https://dx.doi.org/10.1093/imamat/14.3.303
http://cds.cern.ch/record/873507
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author El-Tom, M E A
author_facet El-Tom, M E A
author_sort El-Tom, M E A
collection CERN
description An arbitrarily high-order method for the approximate solution of singular Volterra integral equations of the second kind is presented. The approximate solution is a spline function of degree m, deficiency (m-1), i.e. in the continuity class C, and the method is of order m+1. For m=2 and 3 the method is modified so that the approximate solution is in C/sup 1/. Moreover, an investigation of numerical stability is given and it is shown that, while the above cited methods are numerically stable, methods using spline functions with full continuity are divergent for all m>or=3. (9 refs).
id cern-873507
institution Organización Europea para la Investigación Nuclear
language eng
publishDate 1974
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spelling cern-8735072019-09-30T06:29:59Zdoi:10.1093/imamat/14.3.303http://cds.cern.ch/record/873507engEl-Tom, M E ASpline function approximations to the solution of singular Volterra integral equations of the second kindEngineeringAn arbitrarily high-order method for the approximate solution of singular Volterra integral equations of the second kind is presented. The approximate solution is a spline function of degree m, deficiency (m-1), i.e. in the continuity class C, and the method is of order m+1. For m=2 and 3 the method is modified so that the approximate solution is in C/sup 1/. Moreover, an investigation of numerical stability is given and it is shown that, while the above cited methods are numerically stable, methods using spline functions with full continuity are divergent for all m>or=3. (9 refs).oai:cds.cern.ch:8735071974
spellingShingle Engineering
El-Tom, M E A
Spline function approximations to the solution of singular Volterra integral equations of the second kind
title Spline function approximations to the solution of singular Volterra integral equations of the second kind
title_full Spline function approximations to the solution of singular Volterra integral equations of the second kind
title_fullStr Spline function approximations to the solution of singular Volterra integral equations of the second kind
title_full_unstemmed Spline function approximations to the solution of singular Volterra integral equations of the second kind
title_short Spline function approximations to the solution of singular Volterra integral equations of the second kind
title_sort spline function approximations to the solution of singular volterra integral equations of the second kind
topic Engineering
url https://dx.doi.org/10.1093/imamat/14.3.303
http://cds.cern.ch/record/873507
work_keys_str_mv AT eltommea splinefunctionapproximationstothesolutionofsingularvolterraintegralequationsofthesecondkind

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