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Properties of analytic solution and numerical solution of multi-pantograph equation. (English) Zbl 1059.65060
This paper contains the properties of analytical and numerical solutions of the multi-pantograph equation $$u'(t)=\lambda u(t)+\sum_{i=1}^l u_i u(q_i(t))$$. The sufficient condition of the asymptotic stability, the existence and the uniqueness of the analytical solution of the above equation are obtained. Numerical examples are provided to show that the properties of the $$\theta$$-methods are asymptotically stable if $$\frac12<\theta\leq 1$$.

##### MSC:
 65L05 Numerical methods for initial value problems 65L20 Stability and convergence of numerical methods for ordinary differential equations 34K28 Numerical approximation of solutions of functional-differential equations (MSC2010)
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