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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)=ax(t)+bx([t+1/2]),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:
65L20Stability and convergence of numerical methods for ODE
34K11Oscillation theory of functional-differential equations
34K20Stability theory of functional-differential equations
34K28Numerical approximation of solutions of functional-differential equations
65L03Functional-differential equations (numerical methods)
65L05Initial value problems for ODE (numerical methods)
65L07Numerical investigation of stability of solutions of ODE
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