O(h4) locally overconvergent semidiscrete scheme for the equation ut = uxx + f(t, x, u)
In: Journal of Computational and Applied Mathematics, Jg. 34 (1991-04-01), Heft 2, S. 221-231
Online
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Zugriff:
In the equation ut = uxx + f(t, x, u) the second derivative uxx is approximated by the finite-difference operator Lh which has O(h2) local truncation error at the points h and 1 − h next to the ends of the interval [0, 1] and O(h4) at the interior mesh points 2h, 3h,…, 1 − 2h. It is proved that the obtained semidiscrete scheme is O(h4) globally convergent. The semidiscrete scheme is solved by the pure implicit finite-difference scheme combined with the method of iteration and the Gauss elimination method for tridiagonal matrices. The nonstationary Liouville's equation ut = uxx + e−u has been solved by the proposed algorithm.
| Titel: |
O(h4) locally overconvergent semidiscrete scheme for the equation ut = uxx + f(t, x, u)
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| Autor/in / Beteiligte Person: | Stys, Tadeusz ; Stys, Krystyna |
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| Zeitschrift: | Journal of Computational and Applied Mathematics, Jg. 34 (1991-04-01), Heft 2, S. 221-231 |
| Veröffentlichung: | Elsevier BV, 1991 |
| Medientyp: | unknown |
| ISSN: | 0377-0427 (print) |
| DOI: | 10.1016/0377-0427(91)90044-k |
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