Stability of θ-methods for advanced differential equations with piecewise continuous arguments
نویسندگان
چکیده
منابع مشابه
Stability of Analytic and Numerical Solutions for Differential Equations with Piecewise Continuous Arguments
and Applied Analysis 3 Theorem 2.3. Suppose that f : R ×Rd×Rd → ×Rd is continuous, a, b : R → R are continuous, strictly increasing functions satisfying a 0 b 0 0. Let constants M > 0 and q ∈ 0, 1 exist such that for n ∈ Z, a |x| ≤ V t, x ≤ b |x| , t ∈ R, x ∈ R, 2.3 V n 1, x n 1 ≤ qV n, x n , 2.4 V t, x t ≤ MV n, x n , for t ∈ n, n 1 . 2.5 Then the trivial solution of 1.1 is asymptotically stab...
متن کاملAnalytical Approach to Differential Equations with Piecewise Continuous Arguments via Modified Piecewise Variational Iteration Method
In the present article, we apply the modified piecewise variational iteration method to obtain the approximate analytical solutions of the differential equations with piecewise continuous arguments. This technique provides a sequence of functions which converges to the exact solution of the problem. Moreover, this method reduces the volume of calculations because it does not need discretization...
متن کاملExistence of Piecewise Continuous Mild Solutions for Impulsive Functional Differential Equations with Iterated Deviating Arguments
The objective of this article is to prove the existence of piecewise continuous mild solutions to impulsive functional differential equation with iterated deviating arguments in a Banach space. The results are obtained by using the theory of analytic semigroups and fixed point theorems.
متن کاملStability of numerical solution for partial differential equations with piecewise constant arguments
In this paper, the numerical stability of a partial differential equation with piecewise constant arguments is considered. Firstly, the θ -methods are applied to approximate the original equation. Secondly, the numerical asymptotic stability conditions are given when the mesh ratio and the corresponding parameter satisfy certain conditions. Thirdly, the conditions under which the numerical stab...
متن کاملNumerical Oscillations of Runge-Kutta Methods for Differential Equations with Piecewise Constant Arguments of Alternately Advanced and Retarded Type
The purpose of this paper is to study the numerical oscillations of Runge-Kutta methods for the solution of alternately advanced and retarded differential equations with piecewise constant arguments. The conditions of oscillations for the Runge-Kutta methods are obtained. It is proven that the Runge-Kutta methods preserve the oscillations of the analytic solution. In addition, the relationship ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Computers & Mathematics with Applications
سال: 2005
ISSN: 0898-1221
DOI: 10.1016/j.camwa.2005.02.002