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Convergence of Collocation Method with Delta Functions for Integral Equations of First Kind

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Abstract

Integral equations of first kind with periodic kernels arising in solving partial differential equations by interior source methods are considered. Existence and uniqueness of solution in appropriate spaces of linear analytic functionals is proved. Rate of convergence of collocation method with Dirac’s delta-functions as the trial functions is obtained in case of uniform meshes. In case of an analytic kernel the convergence rate is exponential.

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Authors and Affiliations

  1. University of Tartu, J. Liivi 2, 50409, Tartu, Estonia

    Urve Kangro

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  1. Urve Kangro
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Correspondence to Urve Kangro.

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This work was supported by Estonian Science Foundation under grant No. 5221 and by Estonian Targeted Financing Project SF0180039s08.

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Kangro, U. Convergence of Collocation Method with Delta Functions for Integral Equations of First Kind. Integr. Equ. Oper. Theory 66, 265–282 (2010). https://doi.org/10.1007/s00020-010-1748-0

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  • DOI: https://doi.org/10.1007/s00020-010-1748-0

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