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The Similarity Finite Difference Solutions for Two-Dimensional Parabolic Partial Differential Equations via SOR Iteration

机译：通过SOR迭代的二维抛物线局部微分方程的相似性有限差分解

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摘要

This paper purposely attempts to solve two-dimensional (2D) parabolic partial differential equations (PDEs) using iterative numerical technique. Also, we determine the capability of proposed iterative technique known as Successive Over-Relaxation (SOR) iteration compared to Gauss-Seidel (GS) iteration for solving the 2D parabolic PDEs problem. Firstly, we transform the 2D parabolic PDEs into 2D elliptic PDEs then discretize it using the similarity finite difference (SFD) scheme in order to construct a SFD approximation equation. Then, the SFD approximation equation yields a large-scale and sparse linear system. Next, the linear system is solved by using the proposed iterative numerical technique as described before. Furthermore, the formulation and implementation of SOR iteration are also included. In addition to that, three numerical experiments were carried out to verify the performance of the SOR iteration. Finally, the findings show that the SOR iteration performs better than the GS iteration with less iteration number and computational time.
机译：本文目的地尝试使用迭代数值技术解决二维（2D）抛物线局部微分方程（PDE）。此外，我们确定所谓的迭代技术的能力，与Gauss-Seidel（GS）迭代相比，被称为连续的过度放松（SOR）迭代，用于求解2D抛物线PDES问题。首先，将2D抛物线PDE转换为2D椭圆PDE，然后使用相似度有限差（SFD）方案来分离它以构建SFD近似方程。然后，SFD近似方程产生大规模和稀疏的线性系统。接下来，通过使用之前描述的所提出的迭代数值技术来解决线性系统。此外，还包括制剂和实施SOR迭代。除此之外，还进行了三个数值实验，以验证SOR迭代的性能。最后，调查结果表明，SOR迭代比GS迭代更好地执行，具有较少的迭代号和计算时间。

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