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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) Zbl 1207.65103

J. Comput. Appl. Math. 235, No. 5, 1542-1552 (2011).
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 \(a , b \).
Reviewer: Ivan Secrieru (Chişinău)

Cited in 20 Documents

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

Keywords:

retarded differential equation; weighted difference method; asymptotic stability; oscillations; \(\theta\)-methods; advanced differential equation
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\textit{Q. Wang} et al., J. Comput. Appl. Math. 235, No. 5, 1542--1552 (2011; Zbl 1207.65103)
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References:

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