Approximations of solutions of a class of neutral differential equations with a deviated argument. (English) Zbl 1338.34118
Agrawal, P. N. (ed.) et al., Mathematical analysis and its applications. Proceedings of the international conference on recent trends in mathematical analyis and its applications, ICRTMAA 2014, Roorkee, India, December 21–23, 2014. New Delhi: Springer (ISBN 978-81-322-2484-6/hbk; 978-81-322-2485-3/ebook). Springer Proceedings in Mathematics & Statistics 143, 657-676 (2015).
Summary: We study the approximation of solutions to a class of nonlinear neutral differential equations with a deviated argument in a Hilbert space. We consider an associated integral equation corresponding to the given problem and a sequence of approximate integral equations. We establish the existence and uniqueness of solutions to every approximate integral equation using the fixed point theory. Then, we prove the convergence of the solutions of the approximate integral equations to the solution of the associated integral equation. Next, we consider the Faedo-Galerkin approximations of solutions and prove some convergence results.
For the entire collection see [Zbl 1331.00047].
For the entire collection see [Zbl 1331.00047].
MSC:
| 34K07 | Theoretical approximation of solutions to functional-differential equations |
| 34K30 | Functional-differential equations in abstract spaces |
| 47D06 | One-parameter semigroups and linear evolution equations |
| 47N20 | Applications of operator theory to differential and integral equations |
Keywords:
abstract differential equation with a deviated argument; Banach fixed point theorem; analytic semigroup; Faedo-Galerkin approximationsReferences:
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