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Stability of analytic and numerical solutions for differential equations with piecewise continuous arguments. (English) Zbl 1244.34097
Summary: The asymptotic stability of the analytic and numerical solutions for differential equations with piecewise continuous arguments is investigated by using Lyapunov’s method. In particular, linear equations with variable coefficients are considered. The stability conditions of the analytic solutions of those equations and the numerical solutions of the $\theta$-methods are obtained. Some examples are illustrated.

MSC:
34K20Stability theory of functional-differential equations
34K28Numerical approximation of solutions of functional-differential equations
34K06Linear functional-differential equations
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References:
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