论文标题
非线性方程式的自校正校正胶
Self-similarly corrected Pade approximants for nonlinear equations
论文作者
论文摘要
我们考虑为典型的物理应用的非线性方程找到近似分析解决方案的问题。重点是对Padé近似值的修改，该方法已知为理性函数类提供最佳近似值，但不能提供足够的准确性或根本无法应用于这些非线性问题，其解决方案表现出以不合理功能为特征的行为。为了提高准确性，我们建议一种考虑非理性功能行为的自校正方法。该方法的想法在于将寻求的解决方案表示为两个因素的产物，其中一个是由自相似的根近似物给出的，负责非理性功能行为，而另一个是与有理函数相对应的padé近似值。通过为非线性微分方程构造非常准确的解决方案来说明该方法的效率。进行了彻底的研究，证明所建议的方法比标准帕德近近似值的方法更准确。
We consider the problem of finding approximate analytical solutions for nonlinear equations typical of physics applications. The emphasis is on the modification of the method of Padé approximants that are known to provide the best approximation for the class of rational functions, but do not provide sufficient accuracy or cannot be applied at all for those nonlinear problems, whose solutions exhibit behaviour characterized by irrational functions. In order to improve the accuracy, we suggest a method of self-similarly corrected Padé approximants, taking into account irrational functional behaviour. The idea of the method is in representing the sought solution as a product of two factors, one of which is given by a self-similar root approximant, responsible for irrational functional behaviour, and the other being a Padé approximant corresponding to a rational function. The efficiency of the method is illustrated by constructing very accurate solutions for nonlinear differential equations. A thorough investigation is given proving that the suggested method is more accurate than the method of standard Padé approximants.
