Approximations of solutions for a nonlinear differential equation with a deviating argument

D.N. Pandey, P. Kumar and D. Bahuguna

Applied Mathematics and Computation, 2015, vol. 261, issue C, 242-251

Abstract: In this paper, we prove the existence and convergence of approximate solution for a class of nonlinear differential equations with a deviated argument in a Hilbert space. We establish the existence and uniqueness of a solution to every approximate integral equation using the fixed point argument. Then, we prove the convergence of a solution of the approximate integral equation to the solution of the associated integral equation. We also consider the Faedo–Galerkin approximation of a solution and prove some convergence results.

Keywords: Differential equation with deviated argument; Banach fixed point theorem; Analytic semigroup (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:261:y:2015:i:c:p:242-251

DOI: 10.1016/j.amc.2015.03.071

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