A Shannon Wavelet-Based Approximation Scheme for Thomas–Fermi Models of Confined Atoms and Ions

IF 0.7 4区数学 Q3 MATHEMATICS, APPLIED

Computational Mathematics and Mathematical Physics Pub Date : 2024-06-13 DOI:10.1134/s0965542524700350

Sharda Kumari, Pratik Majhi, M. M. Panja

引用次数: 0

Abstract

An efficient numerical scheme based on the Shannon wavelet basis has been presented here for obtaining highly accurate approximate solutions of Thomas–Fermi equations (TFE) in the finite domain with various initial/boundary conditions (IC/BCs). A point transformation followed by a finite Whittaker Cardinal function approximation (FWCFA) is employed here. The formula relating exponent \(n\) in the desired order of accuracy (\(O{{(10}^{{ - n}}})\)) with the resolution \(J\), the lower and upper limits in the sum of FWCFA have been provided. Examples of TFE with various IC/BCs have been exercised to exhibit the elegance and efficiency of the present scheme.

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基于香农小波的密闭原子和离子托马斯-费米模型近似方案

摘要本文提出了一种基于香农小波基的高效数值方案，用于在有限域中获得具有各种初始/边界条件（IC/BC）的托马斯-费米方程（TFE）的高精度近似解。这里采用的是点变换后的有限惠特克卡迪纳函数近似（FWCFA）。提供了所需精度等级（\(O{(10}^{-n}})\)的指数\(n\)与分辨率\(J\)、FWCFA 总和的下限和上限的相关公式。为了展示本方案的优雅和高效，我们还使用了不同 IC/BC 的 TFE 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

Computational Mathematics and Mathematical Physics MATHEMATICS, APPLIED-PHYSICS, MATHEMATICAL

CiteScore

1.50

自引率

14.30%

发文量

125

审稿时长

4-8 weeks

期刊介绍： Computational Mathematics and Mathematical Physics is a monthly journal published in collaboration with the Russian Academy of Sciences. The journal includes reviews and original papers on computational mathematics, computational methods of mathematical physics, informatics, and other mathematical sciences. The journal welcomes reviews and original articles from all countries in the English or Russian language.