Λεπτομέρειες βιβλιογραφικής εγγραφής
| Τίτλος: |
Preconditioning of pseudospectral method for high-order differential equations. |
| Συγγραφείς: |
Tian, Yan1 (AUTHOR), Liu, Guidong2 (AUTHOR) csu_guidongliu@163.com |
| Πηγή: |
International Journal of Computer Mathematics. Jul2026, Vol. 103 Issue 7, p1563-1582. 20p. |
| Θεματικοί όροι: |
*Jacobi polynomials, *Differential equations, *Integral operators, *Numerical analysis, *Iterative methods (Mathematics), *Interpolation algorithms |
| Περίληψη: |
In this paper, we give two distinct methods for constructing pseudospectral integration matrices based on Birkhoff interpolation. These matrices serve as the exact inverse of the differentiation matrix used in the pseudospectral method introduced by Huang and Sloan [SIAM J. Numer. Anal., 29(1992), pp. 1626–1647]. The proposed pseudospectral integration matrices are employed as preconditioners for the differentiation matrix in pseudospectral methods. Their explicit formulations are given in terms of general Jacobi polynomials. Moreover, the proposed approach can be easily extended to higher-order cases. Numerical experiments confirm that the preconditioned approach significantly improves both the condition number and the accuracy of the approximated solutions. [ABSTRACT FROM AUTHOR] |
| Βάση Δεδομένων: |
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