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Monic Chebyshev pseudospectral differentiation matrices for higher-order IVPs and BVPs: applications to certain types of real-life problems.
- Source :
- Computational & Applied Mathematics; Sep2022, Vol. 41 Issue 6, p1-25, 25p
- Publication Year :
- 2022
-
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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 01018205
- Volume :
- 41
- Issue :
- 6
- Database :
- Complementary Index
- Journal :
- Computational & Applied Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 158609695
- Full Text :
- https://doi.org/10.1007/s40314-022-01940-0