Abstract In this article, we present a new pseudospectral method to approximate the solution of one- and two-dimensional Fisher’s equations, which is a prototype of nonlinear reaction–diffusion equations. The proposed method is based on Chebyshev–Gauss–Lobatto points and employed collocation in both spatial and time direction to study of several travelling wave solutions which evolves into a shock like wavefront and change the shape to some wave pattern. The stability analysis of the proposed method for Fisher’s equation is presented. The numerical results show highly accurate and stable for different values of the reaction rate coefficients. Some model examples of one- and two-dimensional Fisher’s equations are tested and detailed comparison of the proposed method with various other methods are also given.

中文翻译：

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使用伪谱法对 Fisher 方程进行稳定性分析和高精度数值逼近

摘要 在本文中，我们提出了一种新的拟谱方法来近似一维和二维 Fisher 方程的解，这是非线性反应扩散方程的原型。所提出的方法基于切比雪夫-高斯-洛巴托点，并在空间和时间方向上采用搭配来研究几种行波解，这些解演化为类似波前的激波并将形状改变为某种波型。介绍了所提出的Fisher方程方法的稳定性分析。数值结果表明对于不同的反应速率系数值具有高度的准确性和稳定性。测试了一些一维和二维 Fisher 方程的模型示例，并给出了所提出的方法与其他各种方法的详细比较。