Nonlinear Fredholm integral equations and majorant functions

Abstract

From the majorant principle of Kantorovich and the theoretical significance of Newton’s method, we obtain domains of existence and uniqueness of solution for nonlinear Fredholm integral equations, so that these domains are defined from the positive real zeros of a scalar function that we call majorant function. We illustrate this study with three Fredholm integral equations, where separable and nonseparable kernels are involved, by obtaining domains of existence and uniqueness of solution, approximating solutions numerically and giving a priori and a posteriori error estimates of the approximations.

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Correspondence to J. A. Ezquerro.

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This research was partially supported by Ministerio de Economía y Competitividad under grant MTM2014-52016-C2-1-P.

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Ezquerro, J.A., Hernández-Verón, M.A. Nonlinear Fredholm integral equations and majorant functions. Numer Algor 82, 1303–1323 (2019). https://doi.org/10.1007/s11075-019-00656-3

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Keywords

  • Fredholm integral equation
  • Newton’s method
  • Majorant function
  • Domain of existence of solution
  • Domain of uniqueness of solution
  • Error estimates

Mathematics Subject Classification (2010)

  • 45G10
  • 47H99
  • 65J15