A modification of the convergence conditions for Picard's iteration

Ezquerro, J. A.; Hernandez, Miguel A. Lagunas

doi:10.1590/s0101-82052004000100003

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Fredholm Integral Equations With Separable Kernels1

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2022

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Cited by 5 publications

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“…Now, we approach the case of non-separable kernels. In this situation, the successive approximations method [10] and Picard's method [11] are usually applied. In both methods, neither inverse operators nor derivative operators are needed.…”

Section: Fredholm Integral Equations With Separable Kernelsmentioning

confidence: 99%

Improved Iterative Solution of Linear Fredholm Integral Equations of Second Kind via Inverse-Free Iterative Schemes

2020

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This work is devoted to Fredholm integral equations of second kind with non-separable kernels. Our strategy is to approximate the non-separable kernel by using an adequate Taylor’s development. Then, we adapt an already known technique used for separable kernels to our case. First, we study the local convergence of the proposed iterative scheme, so we obtain a ball of starting points around the solution. Then, we complete the theoretical study with the semilocal convergence analysis, that allow us to obtain the domain of existence for the solution in terms of the starting point. In this case, the existence of a solution is deduced. Finally, we illustrate this study with some numerical experiments.

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Section: Fredholm Integral Equations With Separable Kernelsmentioning

confidence: 99%