| dc.contributor.author | Wang, Rong. | en_US |
| dc.date.accessioned | 2014-10-21T12:37:34Z | |
| dc.date.available | 2002 | |
| dc.date.issued | 2002 | en_US |
| dc.identifier.other | AAINQ75710 | en_US |
| dc.identifier.uri | http://hdl.handle.net/10222/55862 | |
| dc.description | In this thesis a high order adaptive method-of-lines package, BACOL, is developed for solving one dimensional parabolic partial differential equations. Collocation with a B-spline basis is used for the spatial discretization. An approximate solution is calculated in a degree p piecewise polynomial subspace, and the spatial error estimate is obtained by using a second solution computed in a degree p+1 piecewise polynomial subspace. | en_US |
| dc.description | BACOL controls both the spatial error and the temporal error. After each time step the spatial error is estimated, and if it is larger than the spatial error tolerance, an equidistribution principle is employed to redistribute the mesh. At the same time, the number of mesh points employed can be changed if necessary. The time integration is done by a differential-algebraic-equation (DAE) solver, DASSL, which uses backward differentiation formulas. Modifications to DASSL included replacing the original linear system solver by the almost block diagonal system solver, COLROW; scaling the Newton iteration matrix to avoid the large condition number generated by the index-1 DAEs; and changing the dimension of tolerance from the number of DAEs to the number of PDEs. Computational results indicate that BACOL is reliable and extremely efficient in dealing with problems having solutions with rapid variation. | en_US |
| dc.description | Thesis (Ph.D.)--Dalhousie University (Canada), 2002. | en_US |
| dc.language | eng | en_US |
| dc.publisher | Dalhousie University | en_US |
| dc.publisher | | en_US |
| dc.subject | Mathematics. | en_US |
| dc.title | High order adaptive collocation software for one-dimensional parabolic partial differential equations. | en_US |
| dc.type | text | en_US |
| dc.contributor.degree | Ph.D. | en_US |
