Faedo–Galerkin approximation of second order nonlinear differential equation with deviated argument

Faedo–Galerkin approximation of second order nonlinear differential equation with deviated... In this manuscript, we consider a second order nonlinear differential equation with deviated argument in a separable Hilbert space X. We used the strongly continuous cosine family of linear operators and fixed point method to study the existence of an approximate solution of the second order differential equation. We define the fractional power of the closed linear operator and used it to prove the convergence of the approximate solution. Also, we prove the existence and convergence of the Faedo–Galerkin approximate solution. Finally, we give an example to illustrate the application of these abstract results. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Computation Elsevier

Faedo–Galerkin approximation of second order nonlinear differential equation with deviated argument

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Publisher
Elsevier
Copyright
Copyright © 2018 Elsevier Inc.
ISSN
0096-3003
eISSN
1873-5649
D.O.I.
10.1016/j.amc.2018.01.060
Publisher site
See Article on Publisher Site

Abstract

In this manuscript, we consider a second order nonlinear differential equation with deviated argument in a separable Hilbert space X. We used the strongly continuous cosine family of linear operators and fixed point method to study the existence of an approximate solution of the second order differential equation. We define the fractional power of the closed linear operator and used it to prove the convergence of the approximate solution. Also, we prove the existence and convergence of the Faedo–Galerkin approximate solution. Finally, we give an example to illustrate the application of these abstract results.

Journal

Applied Mathematics and ComputationElsevier

Published: Jul 15, 2018

References

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