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Solution of partial differential equation of population balance by shifted Legendre polynomials

 

作者: Maw‐Ling Wang,   Rong‐Yeu Chang,  

 

期刊: Journal of the Chinese Institute of Engineers  (Taylor Available online 1983)
卷期: Volume 6, issue 1  

页码: 31-38

 

ISSN:0253-3839

 

年代: 1983

 

DOI:10.1080/02533839.1983.9676720

 

出版商: Taylor & Francis Group

 

数据来源: Taylor

 

摘要:

The batch crystallization processes which are described by partial differential equations of the population density function with appropriate conditions are analyzed. The key method asserts that the population density function can be expressed by a series of shifted Legendre polynomial functions. An effective method which employs a shifted Legendre integral transformation associated with its polynomial functions is applied to solve population balance equations. Making the transformation, the partial differential equation is converted to a series of ordinary differential equations of expansion coefficients. The expansion of the population balance function into shifted Legendre polynomial functions is discussed in detail. The proposed method is straightforward for digital computation and accurate. Illustrative examples are given and compared with the results obtained by the moments method.

 

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