复杂生物膜动力系统的显式有限差分方法研究  

Explicit Finite-difference Method for a Complex Bio-film Dynamics System

作　　者：孙高峰[1] 牛瑞萍[1] 李明[1] 

机构地区：[1]太原理工大学数学学院,太原030024

出　　处：《太原理工大学学报》2015年第6期790-796,共7页Journal of Taiyuan University of Technology

基　　金：国家自然科学基金资助项目:可商业化光滑有限元分析软件的研发(11472184)

摘　　要：针对刻画生物膜成长的动力系统设计了一个非负、有界的显式差分格式,系统是由四个变系数的非线性抛物型偏微分方程组成,描述了营养基质上多种微生物成分间的交互过程;所设计的有限差分格式巧妙地将非线性项转化成线性形式,确保得到的数值解是非负、有界的。最后通过两个数值算例检验了方法的性能,并给出了宏观意义下的数值解的误差。Numerical methods with non-negative and bounded solutions have great significance because of the requirement from many mathematical models with practical background.In this paper,a non-negative and bounded explicit finite-difference scheme is presented for bio-film growth dynamics system.The scheme describes mutual process among different microorganism compositions on nutritional substance and is expressed by four nonlinear parabolic partial differential equations with variable coefficients.The explicit finite-difference scheme neatly transforms the nonlinear form into linear form,which ensures the non-negative and bounded property of solutions.Numerical examples are presented to illustrate the performance of the methods.Error in macro significance is also given.

关 键 词：复杂生物膜系统 非线性反应扩散方程组 显式有限差分法 非负、有界 

分 类 号：O241.82[理学—计算数学]