Using the nonstandard finite difference (NSFD) scheme methodology, we construct a discretization for a parabolic partial differential equation (PDE) having linear advection and diffusion, but with a nonlinear reaction term. The most important requirement is that the scheme produces only non-negative solutions. We show that this can be achieved, and as a consequence, a functional relationship exists between space and time step-sizes. The details of the various term by term NSFD discretizations are discussed.

中文翻译：

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关于修正抛物线反应-平流-扩散 PDE 的正性保持非标准有限差分格式的说明

使用非标准有限差分 (NSFD) 方案方法，我们为具有线性平流和扩散但具有非线性反应项的抛物线偏微分方程 (PDE) 构建离散化。最重要的要求是该方案只产生非负解。我们表明这是可以实现的，因此，空间和时间步长之间存在函数关系。讨论了各种逐项 NSFD 离散化的细节。