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

作者：Pandey D N; Kumar P^*; Bahuguna D

来源：Applied Mathematics and Computation, 2015, 261: 242-251.

DOI：10.1016/j.amc.2015.03.071

• Differential equation with deviated argument
• Banach fixed point theorem
• Analytic semigroup

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.

• 出版日期2015-6-15