Singularity Subtraction for Nonlinear Weakly Singular Integral Equations of the Second Kind

Mario Ahues (), Filomena D. d’Almeida (), Rosário Fernandes () and Paulo B. Vasconcelos ()
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Mario Ahues: Université de Lyon
Filomena D. d’Almeida: Universidade do Porto
Rosário Fernandes: Universidade do Minho
Paulo B. Vasconcelos: Universidade do Porto

Chapter Chapter 1 in Integral Methods in Science and Engineering, 2019, pp 1-13 from Springer

Abstract: Abstract The singularity subtraction technique for computing an approximate solution of a linear weakly singular Fredholm integral equation of the second kind is generalized to the case of a nonlinear integral equation of the same kind. Convergence of the sequence of approximate solutions to the exact one is proved under mild standard hypotheses on the nonlinear factor, and on the sequence of quadrature rules used to build an approximate equation. A numerical example is provided with a Hammerstein operator to illustrate some practical aspects of effective computations.

Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-16077-7_1

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DOI: 10.1007/978-3-030-16077-7_1

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