基于Newton-Maclaurin展开的重正化方法求解二阶差分方程解的瞬态性态
Transient behavior of the solutions to the second order difference equations by the renormalization method based on Newton-Maclaurin expansion
摘要：
应用基于Newton-Maclaurin展开的重正化方法研究了差分方程解趋于定态时的瞬态行为。关键也是自然的一步是使重整化方程是连续的，这样初等函数就可以用来描述差分方程解的瞬态行为。作为具体例子，我们讨论了一类重要的二阶非线性小参数差分方程。结果表明，该方法比多尺度方法更自然。
英文摘要：
The renormalization method based on the Newton-Maclaurin expansion is applied to study the transient behavior of the solutions to the difference equations as they tend to the steady-states. The key and also natural step is to make the renormalization equations to be continuous such that the elementary functions can be used to describe the transient behavior of the solutions to difference equations. As the concrete examples, we deal with the important second order nonlinear difference equations with a small parameter. The result shows that the method is more natural than the multi-scale method.
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