Approximations of Solutions to Abstract Neutral Functional Differential Equation |
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Authors: | Reeta Shukla Dubey |
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Affiliation: | 1. Department of Mathematics , Birla Institute of Technology and Science, Pilani, K. K. Birla Goa Campus , Goa, India reetasd_bits@yahoo.co.in |
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Abstract: | In the present work, we study the approximations of solutions to the abstract neutral functional differential equations with bounded delay. We consider an associated integral equation and a sequence of approximate integral equations. We establish the existence and uniqueness of the solutions to every approximate integral equation using the fixed point arguments. We then 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 the solutions and prove some convergence results. Finally, we demonstrate the application of the results established. |
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Keywords: | Analytic semigroup Contraction mapping theorem Faedo–Galerkin approximation Functional differential equation Mild solution |
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