The main aim of this article is to propose two computational approaches on the basis of the reproducing kernel Hilbert space method for solving singularly perturbed 2D parabolic initial-boundary-value problems. For each approach, the solution in reproducing kernel Hilbert space is constructed with series form, and the approximate solution u_m is given as an m-term summation. Furthermore, convergence of the proposed approaches is presented which provides the theoretical basis of these approaches. Finally, some numerical experiments are considered to demonstrate the efficiency and applicability of proposed approaches.

中文翻译：

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基于再生核理论的奇异摄动二维抛物线初边值问题的数值解：误差和稳定性分析

本文的主要目的是提出两种基于再现核希尔伯特空间方法的计算方法，用于求解奇异扰动二维抛物线初边值问题。对于每一种方法，再现核希尔伯特空间的解都是用级数形式构造的，近似解u _m以m项求和的形式给出。此外，提出了所提出方法的收敛性，为这些方法提供了理论基础。最后，考虑一些数值实验来证明所提出方法的效率和适用性。