AI 中文总结
研究针对非线性反应扩散方程的随机模拟方法，核心方法是在时间离散时采用指数积分器，主要贡献是能产生有效概率，放宽时间步长条件，通过模拟一维和二维模型验证了方法准确性。
AI 中文摘要
通过在空间和时间上离散确定性反应扩散方程，并将离散方程系统中的系数解释为控制移动和反应事件的概率，可以生成随机模拟。本文提出了一种针对非线性反应扩散方程的该方法的新变体，在时间离散时采用指数积分器。该方法产生由适当矩阵函数的项定义的有效概率，无需常用时间离散方案对时间步长的严格条件。针对一维和二维多孔费舍尔型模型给出的模拟结果证明了该方法在多个测试问题上的准确性。
英文摘要
Stochastic simulations can be generated from deterministic reaction-diffusion equations by discretising in space and time and interpreting coefficients in the resulting system of discretised equations as probabilities governing movement and reaction events. In this paper, we present a novel variant of this approach for nonlinear reaction-diffusion equations that employs an exponential integrator when discretising in time. The proposed method yields valid probabilities, defined by the entries of appropriate matrix functions, without the strict conditions on the time step required by a commonly-employed time discretisation scheme. Simulation results presented for one and two dimensional Porous-Fisher type models demonstrate the veracity of the method across several test problems.
Comments9 pages, 2 figures
