Spectral Solutions of Specific Singular Differential Equations Using A Unified Spectral Galerkin-Collocation Algorithm

IF 1.4 4区 物理与天体物理 Q2 MATHEMATICS, APPLIED
H. M. Ahmed, W. M. Abd-Elhameed
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引用次数: 0

Abstract

This paper presents a novel numerical approach to addressing three types of high-order singular boundary value problems. We introduce and consider three modified Chebyshev polynomials (CPs) of the third kind as proposed basis functions for these problems. We develop new derivative operational matrices for the three modified CPs of the third kind by deriving formulas for their first derivatives. Our approach follows a unified method for numerically handling singular differential equations (DEs). To transform these equations into algebraic systems suitable for numerical treatment, we employ the collocation method in combination with the introduced operational matrices of derivatives of the modified CPs of the third kind. We address the convergence examination for the three expansions in a unified manner. We present numerous numerical examples to demonstrate the accuracy and efficiency of our unified numerical approach.

Abstract Image

使用统一谱 Galerkin-Collocation 算法的特定奇异微分方程谱解法
本文提出了一种解决三类高阶奇异边界值问题的新颖数值方法。我们引入并考虑了三个修正的第三类切比雪夫多项式 (CP),作为这些问题的拟议基函数。我们通过推导这三个修正的第三类切比雪夫多项式的一阶导数公式,为它们建立了新的导数运算矩阵。我们的方法遵循数值处理奇异微分方程(DE)的统一方法。为了将这些方程转化为适合数值处理的代数系统,我们结合引入的修正第三类 CP 的导数运算矩阵,采用了搭配法。我们以统一的方式解决了三种展开的收敛性问题。我们列举了大量数值示例,以证明我们的统一数值方法的准确性和高效性。
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来源期刊
Journal of Nonlinear Mathematical Physics
Journal of Nonlinear Mathematical Physics PHYSICS, MATHEMATICAL-PHYSICS, MATHEMATICAL
CiteScore
1.60
自引率
0.00%
发文量
67
审稿时长
3 months
期刊介绍: Journal of Nonlinear Mathematical Physics (JNMP) publishes research papers on fundamental mathematical and computational methods in mathematical physics in the form of Letters, Articles, and Review Articles. Journal of Nonlinear Mathematical Physics is a mathematical journal devoted to the publication of research papers concerned with the description, solution, and applications of nonlinear problems in physics and mathematics. The main subjects are: -Nonlinear Equations of Mathematical Physics- Quantum Algebras and Integrability- Discrete Integrable Systems and Discrete Geometry- Applications of Lie Group Theory and Lie Algebras- Non-Commutative Geometry- Super Geometry and Super Integrable System- Integrability and Nonintegrability, Painleve Analysis- Inverse Scattering Method- Geometry of Soliton Equations and Applications of Twistor Theory- Classical and Quantum Many Body Problems- Deformation and Geometric Quantization- Instanton, Monopoles and Gauge Theory- Differential Geometry and Mathematical Physics
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