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Zbl 1207.65103
Wang, Qi; Zhu, Qingyong; Liu, Mingzhu
Stability and oscillations of numerical solutions for differential equations with piecewise continuous arguments of alternately advanced and retarded type. (English)
[J] J. Comput. Appl. Math. 235, No. 5, 1542-1552 (2011). ISSN 0377-0427

The authors study a differential equation with alternately argument of the form $$x'(t) = a x(t) + b x( [t+1/2]), \quad t>0$$ $$x (0) = x_{0},$$ where $ a,b,x_{0}$ are real constants and [.] denotes the greatest integer function. Using the weighted difference method to solve this problem, conditions of stability and oscillations (for analytical and numerical solutions ) are presented in dependence of coefficients $a , b $.
[Ivan Secrieru (Chişinău)]

MSC 2000:: *65L20 Stability of numerical methods for ODE
34K11 Oscillation theory of functional-differential equations
34K20 Stability theory of functional-differential equations
34K28 Numerical approximation of solutions of FDE
65L03
65L05 Initial value problems for ODE (numerical methods)
65L07 Numerical investigation of stability of solutions of ODE

Keywords: retarded differential equation; weighted difference method; asymptotic stability; oscillations; $\theta$-methods; advanced differential equation

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