The aim of this research work is to obtain the numerical solution of Fisher’s equation using the radial basis function (RBF) with pseudospectral method (RBF-PS). The two optimization techniques, namely, particle swarm optimization (PSO) and artificial bee colony (ABC), have been compared for the numerical results in terms of errors, which are employed to find the shape parameter of the RBF. Two problems of Fisher’s equation are presented to test the accuracy of the method, and the obtained numerical results are compared to verify the effectiveness of this novel approach. The calculation of the error norms leads to the conclusion that the performance of PSO is better than the ABC algorithm to minimize the error for the shape parameter in a given range.

中文翻译：

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Fisher方程数值分析的粒子群优化与人工蜂群算法对比研究

这项研究工作的目的是使用径向基函数（RBF）和伪谱方法（RBF-PS）获得Fisher方程的数值解。比较了两种优化技术，即粒子群优化（PSO）和人工蜂群（ABC）的数值结果的误差，并用于寻找 RBF 的形状参数。提出了费舍尔方程的两个问题来测试该方法的准确性，并对所得数值结果进行比较以验证该新方法的有效性。误差范数的计算得出这样的结论：对于给定范围内的形状参数的误差最小化，PSO 的性能优于 ABC 算法。