Ta Catherine, Wang Dongyong, Nie Qing
Department of Mathematics, University of California, Center for Mathematical and Computational Biology, Center for Complex Biological Systems, Irvine, CA 92697, USA.
J Comput Phys. 2015 Aug 15;295:505-522. doi: 10.1016/j.jcp.2015.04.028.
Stochastic effects are often present in the biochemical systems involving reactions and diffusions. When the reactions are stiff, existing numerical methods for stochastic reaction diffusion equations require either very small time steps for any explicit schemes or solving large nonlinear systems at each time step for the implicit schemes. Here we present a class of semi-implicit integration factor methods that treat the diffusion term exactly and reaction implicitly for a system of stochastic reaction-diffusion equations. Our linear stability analysis shows the advantage of such methods for both small and large amplitudes of noise. Direct use of the method to solving several linear and nonlinear stochastic reaction-diffusion equations demonstrates good accuracy, efficiency, and stability properties. This new class of methods, which are easy to implement, will have broader applications in solving stochastic reaction-diffusion equations arising from models in biology and physical sciences.
随机效应常常出现在涉及反应和扩散的生化系统中。当反应是刚性的时，现有的用于随机反应扩散方程的数值方法，对于任何显式格式都需要非常小的时间步长，或者对于隐式格式在每个时间步长都要求解大型非线性系统。在此，我们提出一类半隐式积分因子方法，该方法对于随机反应扩散方程组精确处理扩散项而隐式处理反应项。我们的线性稳定性分析表明了此类方法在噪声幅度大小两种情况下的优势。直接使用该方法求解几个线性和非线性随机反应扩散方程展现出良好的精度、效率和稳定性。这类易于实现的新方法在求解生物学和物理科学模型中产生的随机反应扩散方程方面将有更广泛的应用。
