Taylor wavelet analysis and numerical simulation for boundary value problems of higher order under multiple boundary conditions

IF 1.9 4区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY
Pramana Pub Date : 2024-11-06 DOI:10.1007/s12043-024-02825-z
Ashish Rayal, Prerna Negi, Shailendra Giri, Haci Mehmet Baskonus
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引用次数: 0

Abstract

The predominant objective of this study is to simulate higher-order linear and nonlinear initial-boundary value problems using approximation and collocation approach with the bases of Taylor wavelet. Differentiation is utilised in the function approximation approach to acquire expression for higher-order derivatives as well as solution to an unknown function. The mentioned scheme of wavelet approximation for higher-order differential equations is an intriguing scheme that has the potential to produce accurate and efficient results. The flexibility of the wavelet to the local character of differential equations of higher order corresponds well with the complexity caused by various boundary conditions. This study investigates the effectiveness of wavelet-based approach in solving higher-order differential equations under appropriate initial conditions, boundary conditions and Robin boundary conditions. Furthermore, a thorough error analysis is required to assess the dependability of these solutions. Therefore, maximum and minimum absolute errors, \(L_{2}\) errors, relative error and experimental convergence order at various wavelet bases are evaluated to investigate the performance and effectiveness of the mentioned scheme. We have also compared the approximated solutions with other existing solutions to demonstrate the reliability and accuracy of the mentioned scheme.

多边界条件下高阶边界值问题的泰勒小波分析和数值模拟
本研究的主要目的是利用泰勒小波为基础的近似和配位方法模拟高阶线性和非线性初界值问题。函数逼近法利用微分来获取高阶导数的表达式以及未知函数的解。上述高阶微分方程的小波逼近方案是一种有趣的方案,有可能产生精确而高效的结果。小波对高阶微分方程局部特性的灵活性与各种边界条件造成的复杂性相吻合。本研究探讨了基于小波的方法在适当的初始条件、边界条件和罗宾边界条件下求解高阶微分方程的有效性。此外,还需要进行全面的误差分析,以评估这些解法的可靠性。因此,我们评估了不同小波基的最大和最小绝对误差、(L_{2}\)误差、相对误差和实验收敛阶数,以研究上述方案的性能和有效性。我们还将近似解与其他现有解进行了比较,以证明上述方案的可靠性和准确性。
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
Pramana
Pramana 物理-物理:综合
CiteScore
3.60
自引率
7.10%
发文量
206
审稿时长
3 months
期刊介绍: Pramana - Journal of Physics is a monthly research journal in English published by the Indian Academy of Sciences in collaboration with Indian National Science Academy and Indian Physics Association. The journal publishes refereed papers covering current research in Physics, both original contributions - research papers, brief reports or rapid communications - and invited reviews. Pramana also publishes special issues devoted to advances in specific areas of Physics and proceedings of select high quality conferences.
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