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Geometric meshes in collocation methods for Volterra integral equations with proportional time delays

by H. Brunner and Q. Hu and Q. Lin

(Report number 1999-25)

Abstract
In this paper we introduce new kind of nonuniform mesh, the so-called geometric mesh, and discuss the corresponding collocation method for Volterra integral equations of the second kind with proportional delay of the form $qt$ ($0 < q < 1$). It will be shown that, in contrast to the uniform mesh, the iterated collocation solution associated with such a mesh exhibits almost optimal superconvergence at the mesh points, provided that collocation parameters are chosen as the Gauss points in $(0,1)$.

Keywords: Delay integral equation, geometric mesh, collocation method, iterated collocation solution, superconvergence

@Techreport{BHL99_259,
  author = {H. Brunner and Q. Hu and Q. Lin},
  title = {Geometric meshes in collocation methods for Volterra integral equations with proportional time delays},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {1999-25},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports1999/1999-25.pdf },
  year = {1999}
}

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