Discrete projection methods for Fredholm–Hammerstein integral equations using Kumar and Sloan technique

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-03-26 DOI:10.1007/s10092-024-00573-5

Ritu Nigam, Nilofar Nahid, Samiran Chakraborty, Gnaneshwar Nelakanti

引用次数: 0

Abstract

The proposed work discusses discrete collocation and discrete Galerkin methods for second kind Fredholm–Hammerstein integral equations on half line \([0,\infty )\) using Kumar and Sloan technique. In addition, the finite section approximation method is applied to transform the domain of integration from \([0, \infty )\) to \([0,\alpha ],~ \alpha >0\). In contrast to previous studies in which the optimal order of convergence is achieved for projection methods, we attained superconvergence rates in uniform norm using piecewise polynomial basis function. Moreover, these superconvergence rates are further enhanced by using discrete multi-projection (collocation and Galerkin) methods. In order to support the provided theoretical framework, numerical examples are included as well.

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使用 Kumar 和 Sloan 技术的 Fredholm-Hammerstein 积分方程离散投影法

本文利用 Kumar 和 Sloan 技术讨论了半线 \([0,\infty )\) 上第二类 Fredholm-Hammerstein 积分方程的离散配位和离散 Galerkin 方法。此外，还应用了有限截面近似法将积分域从\([0, \infty )\)转换为\([0,\alpha ],~ \alpha >0\)。与以往研究中的投影方法达到最佳收敛阶数不同，我们使用片断多项式基函数达到了均匀法的超收敛率。此外，通过使用离散多投影（配位和 Galerkin）方法，这些超收敛率得到了进一步提高。为了支持所提供的理论框架，我们还提供了数值示例。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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