Monic Chebyshev pseudospectral differentiation matrices for higher-order IVPs and BVPs: applications to certain types of real-life problems
Computational & Applied Mathematics
; 41(6):25, 2022.
Article
in English
| Web of Science | ID: covidwho-1976889
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.
Monic Chebyshev polynomials; Pseudospectral differentiation matrices; Convergence and error analysis; Higher-order IVPs and BVPs; MHD; COVID-19; Monic Chebyshev polynomials; Pseudospectral differentiation; matrices; Convergence and error analysis; Higher-order IVPs and BVPs; MHD; COVID-19; equations; boundary; Mathematics
Full text:
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Collection:
Databases of international organizations
Database:
Web of Science
Language:
English
Journal:
Computational & Applied Mathematics
Year:
2022
Document Type:
Article
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