This work presents two different finite difference methods to compute the numerical solutions for Newell–Whitehead–Segel partial differential equation, which are implicit exponential finite difference method and fully implicit exponential finite difference method. Implicit exponential methods lead to nonlinear systems. Newton method is used to solve the resulting systems. Stability and consistency are discussed. To illustrate the accuracy of the proposed numerical methods, some examples are delivered at the end.

中文翻译：

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求解Newell-Whitehead-Segel方程的指数有限差分法

这项工作提出了两种不同的有限差分方法来计算Newell-Whitehead-Segel偏微分方程的数值解，它们是隐式指数有限差分方法和完全隐式指数有限差分方法。隐式指数方法导致非线性系统。牛顿法用于求解所得系统。讨论了稳定性和一致性。为了说明所提出的数值方法的准确性，最后提供了一些示例。