Adaptive Optimal m-Stage Runge-Kutta Methods for Solving Reaction-Diffusion-Chemotaxis Systems

المؤلف

Yu, Jui-Ling

المصدر

Journal of Applied Mathematics

العدد

المجلد 2011، العدد 2011 (31 ديسمبر/كانون الأول 2011)، ص ص. 1-25، 25ص.

الناشر

Hindawi Publishing Corporation

تاريخ النشر

2011-06-28

دولة النشر

مصر

عدد الصفحات

25

التخصصات الرئيسية

الرياضيات

الملخص EN

We present a class of numerical methods for the reaction-diffusion-chemotaxis system which is significant for biological and chemistry pattern formation problems.

To solve reaction-diffusion-chemotaxis systems, efficient and reliable numerical algorithms are essential for pattern generations.

Along with the implementation of the method of lines, implicit or semi-implicit schemes are typical time stepping solvers to reduce the effect on time step constrains due to the stability condition.

However, these two schemes are usually difficult to employ.

In this paper, we propose an adaptive optimal time stepping strategy for the explicit m-stage Runge-Kutta method to solve reaction-diffusion-chemotaxis systems.

Instead of relying on empirical approaches to control the time step size, variable time step sizes are given explicitly.

Yet, theorems about stability and convergence of the algorithm are provided in analyzing robustness and efficiency.

Numerical experiment results on a testing problem and a real application problem are shown.

نمط استشهاد جمعية علماء النفس الأمريكية (APA)

Yu, Jui-Ling. 2011. Adaptive Optimal m-Stage Runge-Kutta Methods for Solving Reaction-Diffusion-Chemotaxis Systems. Journal of Applied Mathematics،Vol. 2011, no. 2011, pp.1-25.
https://search.emarefa.net/detail/BIM-468210

نمط استشهاد الجمعية الأمريكية للغات الحديثة (MLA)

Yu, Jui-Ling. Adaptive Optimal m-Stage Runge-Kutta Methods for Solving Reaction-Diffusion-Chemotaxis Systems. Journal of Applied Mathematics No. 2011 (2011), pp.1-25.
https://search.emarefa.net/detail/BIM-468210

نمط استشهاد الجمعية الطبية الأمريكية (AMA)

Yu, Jui-Ling. Adaptive Optimal m-Stage Runge-Kutta Methods for Solving Reaction-Diffusion-Chemotaxis Systems. Journal of Applied Mathematics. 2011. Vol. 2011, no. 2011, pp.1-25.
https://search.emarefa.net/detail/BIM-468210

نوع البيانات

مقالات

لغة النص

الإنجليزية

الملاحظات

Includes bibliographical references

رقم السجل

BIM-468210