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- Title
Spectral Solutions of Specific Singular Differential Equations Using A Unified Spectral Galerkin-Collocation Algorithm.
- Authors
Ahmed, H. M.; Abd-Elhameed, W. M.
- 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.
- Subjects
DIFFERENTIAL equations; ALGEBRAIC equations; BOUNDARY value problems; MATRICES (Mathematics); COLLOCATION methods; RICCATI equation
- Publication
Journal of Nonlinear Mathematical Physics, 2024, Vol 31, Issue 1, p1
- ISSN
1402-9251
- Publication type
Article
- DOI
10.1007/s44198-024-00194-0