A detailed comparison is made between four different iterative procedures: Picard, Ishikawa, Mann and Picard-Krasnoselskii, within the framework of the BLUES function method and the variational iteration method. The resulting modified methods are subsequently applied to a nonlinear reaction-diffusion-advection differential equation to generate approximations to the known exact solution. The differences between the BLUES function method and the variational iteration method are illustrated by studying the approximants and the error between the obtained approximants and the exact solution.
翻译:对四种不同的迭接程序进行了详细比较:Picard、Ishikawa、Mann和Picard-Krasnoselskii, 在BLUES函数法和变异迭代法的框架内, 由此产生的修改方法随后适用于非线性反射反射- 扩散- 适应差异方程式, 以生成已知确切解决方案的近似值。 BLUES函数法和变异迭代法之间的差异通过研究近似物和获得的近似物与确切解决方案之间的差错来说明。