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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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