Abstract
This study probes into the existence of a unique solution and the numerical approximation of a nonlinear functional Volterra–Fredholm integral equations of the mixed type and second kind. Based on the Lipschitz constants of the functional and kernel, a Bielecki’s norm is defined and used to modify a distance inequality on a constructed self-map. The map is shown to be contractive, thereby establishing solvability. The problem is then approximated by collocating at discrete points and use of a composite multidimensional numerical quadrature approximation. A new Grönwall-type inequality is proposed, and used, to prove the second order of convergence of the numerical scheme. Numerical experiments are provided to verify the theoretical results.
Citation
Chinedu Nwaigwe. "SOLVABILITY AND APPROXIMATION OF NONLINEAR FUNCTIONAL MIXED VOLTERRA–FREDHOLM EQUATION IN BANACH SPACE." J. Integral Equations Applications 34 (4) 489 - 500, Winter 2022. https://doi.org/10.1216/jie.2022.34.489
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