论文标题
Smoluchowski的聚合方程的一种新颖的优化分解方法
A Novel Optimized Decomposition Method for Smoluchowski's Aggregation Equation
论文作者
论文摘要
Smoluchowski的聚合方程在Bio-Pharmaceuticals \ Cite {Zidar2018Characterisation}，金融领域\ Cite {Pushkin2004571}，Aerosol Science \ Cite {Shen2020效率}和许多其他领域中具有应用。已经设计了几种分析，数值和半分析方法来计算该方程的解决方案。半分析方法通常使用，因为它们不需要空间变量的离散化。本文介绍了一种新型的半分析技术，称为优化分解方法（ODM）（请参阅\ cite {odibat2020220Optimizatized}）来计算这种相关的内部派系微分方程的解决方案。使用ODM计算出的串联解决方案显示为精确解决方案。理论结果是使用数值示例来验证的，用于科学相关的聚合内核，可获得确切的解决方案。此外，将ODM近似结果与使用\ cite {Singh2015adomian}中的Adomian分解方法（ADM）获得的溶液进行了比较。对于所考虑的示例，新方法显示出比ADM优越，因此将其确立为解决Smoluchowski方程的改进和有效方法。
The Smoluchowski's aggregation equation has applications in the field of bio-pharmaceuticals \cite{zidar2018characterisation}, financial sector \cite{PUSHKIN2004571}, aerosol science \cite{shen2020efficient} and many others. Several analytical, numerical and semi-analytical approaches have been devised to calculate the solutions of this equation. Semi-analytical methods are commonly employed since they do not require discretization of the space variable. The article deals with the introduction of a novel semi-analytical technique called the optimized decomposition method (ODM) (see \cite{odibat2020optimized}) to compute solutions of this relevant integro-partial differential equation. The series solution computed using ODM is shown to converge to the exact solution. The theoretical results are validated using numerical examples for scientifically relevant aggregation kernels for which the exact solutions are available. Additionally, the ODM approximated results are compared with the solutions obtained using the Adomian decomposition method (ADM) in \cite{singh2015adomian}. The novel method is shown to be superior to ADM for the examples considered and thus establishes as an improved and efficient method for solving the Smoluchowski's equation.
