We suggest the local analysis of a class of iterative schemes based on decomposition technique for solving Banach space valued nonlinear models. Earlier results used hypotheses up to the fourth derivative to establish convergence. But we only apply the first derivative in our convergence theorem. We also provide computable radius of convergence ball, error estimates and uniqueness of the solution results not studied in earlier works. Hence, we enhance the applicability of these schemes. Furthermore, we explore, using basin of attraction tool, the dynamics of the schemes when they are applied on various complex polynomials. This article is concluded with numerical experiments.

我们建议对一类基于分解技术的迭代方案进行局部分析，以求解 Banach 空间值非线性模型。较早的结果使用直到四阶导数的假设来建立收敛。但是我们只在收敛定理中应用一阶导数。我们还提供了可计算的收敛球半径、误差估计和早期工作中未研究过的解结果的唯一性。因此，我们增强了这些方案的适用性。此外，我们使用吸引池工具探索了将方案应用于各种复杂多项式时的动态。本文以数值实验结束。