CAJ | 학술논문

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。
침대각화생물막성장적동력계통설계료일개비부、유계적현식차분격식，계통시유사개변계수적비선성포물형편미분방정조성，묘술료영양기질상다충미생물성분간적교호과정；소설계적유한차분격식교묘지장비선성항전화성선성형식，학보득도적수치해시비부、유계적。최후통과량개수치산례검험료방법적성능，병급출료굉관의의하적수치해적오차。
Numerical methods with non‐negative and bounded solutions have great significance because of the requirement from many mathematical models with practical background .In this pa‐per ,a non‐negative and bounded explicit finite‐difference scheme is presented for bio‐film grow th dynamics system .The scheme describes mutual process among different microorganism composi‐tions on nutritional substance and is expressed by four nonlinear parabolic partial differential e‐quations with variable coefficients .The explicit finite‐difference scheme neatly transforms the nonlinear form into linear form ,w hich ensures the non‐negative and bounded property of solu‐tions .Numerical examples are presented to illustrate the performance of the methods .Error in macro significance is also given .