Solving Advection Equations by Applying the Crank-Nicolson Scheme Combined with the Richardson Extrapolation
Advection equations appear often in large-scale mathematical models arising in many fields of science and engineering. The Crank-Nicolson scheme can successfully be used in the numerical treatment of such equations. The accuracy of the numerical solution can sometimes be increased substantially by a...
Saved in:
| Main Authors: | , , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2011-01-01
|
| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2011/520840 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832553407054872576 |
|---|---|
| author | Zahari Zlatev Ivan Dimov István Faragó Krassimir Georgiev Ágnes Havasi Tzvetan Ostromsky |
| author_facet | Zahari Zlatev Ivan Dimov István Faragó Krassimir Georgiev Ágnes Havasi Tzvetan Ostromsky |
| author_sort | Zahari Zlatev |
| collection | DOAJ |
| description | Advection equations appear often in large-scale mathematical models arising in many fields of science and engineering. The Crank-Nicolson scheme can successfully be used in the numerical treatment of such equations. The accuracy of the numerical solution can sometimes be increased substantially by applying the Richardson Extrapolation. Two theorems related to the accuracy of the calculations will be formulated and proved in this paper. The usefulness of the combination consisting of the Crank-Nicolson scheme and the Richardson Extrapolation will be illustrated by numerical examples. |
| format | Article |
| id | doaj-art-7e3e9100742a46669af75725fbc6dee8 |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-7e3e9100742a46669af75725fbc6dee82025-02-03T05:54:08ZengWileyInternational Journal of Differential Equations1687-96431687-96512011-01-01201110.1155/2011/520840520840Solving Advection Equations by Applying the Crank-Nicolson Scheme Combined with the Richardson ExtrapolationZahari Zlatev0Ivan Dimov1István Faragó2Krassimir Georgiev3Ágnes Havasi4Tzvetan Ostromsky5National Environmental Research Institute, Aarhus University, DK-4000 Roskilde, DenmarkInstitute of Information and Communication Technologies, Bulgarian Academy of Sciences, BG-1113 Sofia, BulgariaDepartment of Applied Analysis and Computational Mathematics, Eötvös Loránd University, H-1117 Budapest, HungaryInstitute of Information and Communication Technologies, Bulgarian Academy of Sciences, BG-1113 Sofia, BulgariaDepartment of Meteorology, Eötvös Loránd University, H-1117 Budapest, HungaryInstitute of Information and Communication Technologies, Bulgarian Academy of Sciences, BG-1113 Sofia, BulgariaAdvection equations appear often in large-scale mathematical models arising in many fields of science and engineering. The Crank-Nicolson scheme can successfully be used in the numerical treatment of such equations. The accuracy of the numerical solution can sometimes be increased substantially by applying the Richardson Extrapolation. Two theorems related to the accuracy of the calculations will be formulated and proved in this paper. The usefulness of the combination consisting of the Crank-Nicolson scheme and the Richardson Extrapolation will be illustrated by numerical examples.http://dx.doi.org/10.1155/2011/520840 |
| spellingShingle | Zahari Zlatev Ivan Dimov István Faragó Krassimir Georgiev Ágnes Havasi Tzvetan Ostromsky Solving Advection Equations by Applying the Crank-Nicolson Scheme Combined with the Richardson Extrapolation International Journal of Differential Equations |
| title | Solving Advection Equations by Applying the Crank-Nicolson Scheme Combined with the Richardson Extrapolation |
| title_full | Solving Advection Equations by Applying the Crank-Nicolson Scheme Combined with the Richardson Extrapolation |
| title_fullStr | Solving Advection Equations by Applying the Crank-Nicolson Scheme Combined with the Richardson Extrapolation |
| title_full_unstemmed | Solving Advection Equations by Applying the Crank-Nicolson Scheme Combined with the Richardson Extrapolation |
| title_short | Solving Advection Equations by Applying the Crank-Nicolson Scheme Combined with the Richardson Extrapolation |
| title_sort | solving advection equations by applying the crank nicolson scheme combined with the richardson extrapolation |
| url | http://dx.doi.org/10.1155/2011/520840 |
| work_keys_str_mv | AT zaharizlatev solvingadvectionequationsbyapplyingthecranknicolsonschemecombinedwiththerichardsonextrapolation AT ivandimov solvingadvectionequationsbyapplyingthecranknicolsonschemecombinedwiththerichardsonextrapolation AT istvanfarago solvingadvectionequationsbyapplyingthecranknicolsonschemecombinedwiththerichardsonextrapolation AT krassimirgeorgiev solvingadvectionequationsbyapplyingthecranknicolsonschemecombinedwiththerichardsonextrapolation AT agneshavasi solvingadvectionequationsbyapplyingthecranknicolsonschemecombinedwiththerichardsonextrapolation AT tzvetanostromsky solvingadvectionequationsbyapplyingthecranknicolsonschemecombinedwiththerichardsonextrapolation |