Iterative Approximation of Nonlinear Fredholm Integral Equations of the Second Kind by Picard’s Method
Keywords:
Fredholm integral equations, Picard’s iteration, Lipschitz continuity, Fréchet derivativeAbstract
This study on Iterative Approximation of Nonlinear Fredholm Integral Equations of the Second Kind by Picard's Method considers the application of Picard’s iteration scheme for the approximation of an operator equation in Banach space. Using Lipschitz continuity condition and the prescribed auxiliary scalar function, the location of existence of solution for nonlinear integral equation Fredholm type and second kind is obtained. The error estimate provided in the analysis is used to predict the convergence speed of the Picard’s scheme. An indication from the error estimate shows that the error will be totally insignificant after eight iterations.
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