Stability of numerical solution for partial differential equations with piecewise constant arguments
نویسندگان
چکیده
منابع مشابه
Stability 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...
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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...
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ژورنال
عنوان ژورنال: Advances in Difference Equations
سال: 2018
ISSN: 1687-1847
DOI: 10.1186/s13662-018-1514-1