Monic Chebyshev Pseudospectral Differentiation Matrices for Higher-Order Ivps and Bvps: Applications To Certain Types of Real-Life Problems
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Date
2022
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Publisher
Springer Heidelberg
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HYBRID
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Yes
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Abstract
We introduce new differentiation matrices based on the pseudospectral collocation method. Monic Chebyshev polynomials (MCPs) were used as trial functions in differentiation matrices (D-matrices). Those matrices have been used to approximate the solutions of higher-order ordinary differential equations (H-ODEs). Two techniques will be used in this work. The first technique is a direct approximation of the H-ODE. While the second technique depends on transforming the H-ODE into a system of lower order ODEs. We discuss the error analysis of these D-matrices in-depth. Also, the approximation and truncation error convergence have been presented to improve the error analysis. Some numerical test functions and examples are illustrated to show the constructed D-matrices' efficiency and accuracy.
Description
Abdelhakem, Mohamed/0000-0001-7085-1685
ORCID
Keywords
Monic Chebyshev Polynomials, Pseudospectral Differentiation Matrices, Convergence And Error Analysis, Higher-Order Ivps And Bvps, Mhd, Covid-19, Composite material, Truncation (statistics), Ode, Orthogonal polynomials, Economics, Matrix (chemical analysis), Collocation (remote sensing), Mathematical analysis, Polynomial, Article, Differential equation, Numerical Integration Methods for Differential Equations, Machine learning, FOS: Mathematics, Chebyshev filter, Anomalous Diffusion Modeling and Analysis, Economic growth, Matrix Algorithms and Iterative Methods, Numerical Analysis, Classical orthogonal polynomials, Statistics, Chebyshev equation, Applied mathematics, Computer science, Materials science, Truncation error, Computational Theory and Mathematics, Modeling and Simulation, Computer Science, Physical Sciences, Convergence (economics), Monic polynomial, Chebyshev polynomials, Mathematics, Ordinary differential equation, Matrix Computations, MHD, Other special orthogonal polynomials and functions, convergence and error analysis, higher-order IVPs and BVPs, pseudospectral differentiation matrices, monic Chebyshev polynomials, Numerical solution of boundary value problems involving ordinary differential equations, Spectral methods applied to problems in fluid mechanics, COVID-19, Stability and convergence of numerical methods for ordinary differential equations
Fields of Science
01 natural sciences, 0103 physical sciences, 0101 mathematics
Citation
Abdelhakem M.;...et.al. (2022). "Monic Chebyshev pseudospectral differentiation matrices for higher-order IVPs and BVPs: applications to certain types of real-life problems", Computational and Applied Mathematics, Vol.41,No.6.
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OpenCitations Citation Count
24
Source
Computational and Applied Mathematics
Volume
41
Issue
6
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Scopus : 27
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