演示方案

演示方案
然而,为了演示解决方案的行为与εt≥0,应将其他^ +,为不同的领域。上述方程可以证明如下双方通过日志(Krippendorff,2004)。渐近逼近理论极大地扩大了治疗的摄动问题,证明在附录图1。O(e / t)是小相比其他条款和扩张是只局限于预测当tε依赖的间隔I_εε/ t很小。例如,如果I_ε=(√ε,∞)然后tϵI_ε表明ε/ t <√ε然而提供的扩张并不扩大初始条件,导致其他几个概念的引入提供了文学(桑德斯et al .,2007)一般来说,逼近渐近级数在一些特定的间隔I_ε渐近级数的表达式,证明如下:。然而,对于每个m值将自然数N更为强大的条件可以证明了如下的错误是被认为是第一个省略词的顺序。只是发现,某些形式的渐近级数可以庞加莱等独特的渐近级数的φ^ n可以独立的ε与下面的例子演示了(桑德斯et al .,2007)。 演示方案 However, in order to demonstrate the behavior of the solution with ε for t ≥ 0, it is required to divide theR^+, into different domains. The above equation can be demonstrated as follows by taking the log on both sides(Krippendorff, 2004). The theory of asymptotic approximation has expanded greatly in treating with the perturbation problems as demonstrated in figure 1 in appendix. Where the O (e/t) is the small as compared to the other terms and this expansion is only predictable when t is confined to the ε dependent interval I_ε in the way that ε/t is small. For example, if I_ε = (√ε,∞) then t ϵI_ε that demonstrates that the ε/t<√ε however the provided expansion does not expand the initial condition and leads to the introduction of the several other concepts in the provided literature(Sanders et al., 2007)Generally, the approximation asymptotic series on some particular interval I_ε where the asymptotic series is the expression that is demonstrated as follows:. However, for each m value which will be the natural number N the much stronger condition can be demonstrated as follows which is considered as the error is of the order of the first omitted term.It is identified that only some forms of asymptotic series can be unique such as Poincare asymptotic series where the φ^n can be independent of ε as demonstrated with the following example(Sanders et al., 2007).