## Stability and oscillations of numerical solutions for differential equations with piecewise continuous arguments of alternately advanced and retarded type.(English)Zbl 1207.65103

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 $$a , b$$.

### MSC:

 65L20 Stability and convergence of numerical methods for ordinary differential equations 34K11 Oscillation theory of functional-differential equations 34K20 Stability theory of functional-differential equations 34K28 Numerical approximation of solutions of functional-differential equations (MSC2010) 65L03 Numerical methods for functional-differential equations 65L05 Numerical methods for initial value problems involving ordinary differential equations 65L07 Numerical investigation of stability of solutions to ordinary differential equations
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### References:

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