Abstract
This work is concerned with spectral Jacobi-collocation methods for Volterra integral equations of the second kind with a weakly singular of the form (t-s)-α. When the underlying solutions are sufficiently smooth, the convergence analysis was carried out in [Chen & Tang, J. Comput. Appl. Math., 233 (2009), pp. 938-950]; due to technical reasons the results are restricted to 0 < μ < 1/2 In this work, we will improve the results to the general case 0 < μ < 1 and demonstrate that the numerical errors decay exponentially in the infinity and weighted norms when the smooth solution is involved.
Original language | English |
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Pages (from-to) | 47-56 |
Number of pages | 10 |
Journal | Journal of Computational Mathematics |
Volume | 31 |
Issue number | 1 |
DOIs | |
Publication status | Published - Jan 2013 |
Scopus Subject Areas
- Computational Mathematics
User-Defined Keywords
- Convergence analysis
- Spectral-collocation methods
- Volterra integral equations