Time stepping algorithms for parabolic partial differential equations
| Author | Abdulla, Thuraya Juma | |
|---|---|---|
| metadata.dc.contributor.department | University of Bahrain, College of Science Department of Mathematics | |
| metadata.dc.date.accessioned | 2026-09-20T15:50:35Z | |
| Publication date | 1995 | |
| Degree level | Master | |
| Abstract | Abstract : A number of time stepping algorithms for solving parabolic partial differential equations (PDEs) in one and two space dimensions are studied. The parabolic partial differential equation is transformed into a system of ordinary differential equatiors (ODEs) via method of lines approach (MOL). The solution of the system of ODEs satisfies a recurrence relation which involves matrix exponential functions. Padé approximants are empolyed to approximate such exponential terms. It is shown [9] that methods based on (1,1) diagonal Padé aproximant suffer with time steps restriction for problems with high frequency components in the solution when a time discretization is imposed with steps that are "too large" relative to the spatial discretization. A monotonicity property is established for all diagonal Padé approximants from which it is shown that corresponding higher-order methods suffer a similar time step restriction as the (1,1) Padé. Next, various high-order methods based on subdiagonal Padé approximations are presented which, through a partial fraction expansion, are no more complicated to implement than the first order implicit Euler method based on the (1,0) Padé approximation; moreover, the resulting algorithms are free of a time step restriction intrinsic to those based on diagonal Padé approximations [7]. Splitting methods based on the (1,0) and (1,1) Padé approximants are considered in two space dimension with homogeneous and time dependent boundary conditions [9], [18]. All computations are performed on VAX machine, University of Bahrain. Packages, such as, Mathematica and Spyglass are used for symbolic computation and graphics. | |
| metadata.dc.identifier.other | Drupal node 4165 | |
| metadata.dc.identifier.other | https://digitalrepository.uob.edu.bh/en/dar/time-stepping-algorithms-parabolic-partial-differential-equations | |
| metadata.dc.identifier.uri | http://165.227.56.122/handle/123456789/7014 | |
| Language | en | |
| Link | https://digitalrepository.uob.edu.bh/en/_flysystem/fedora/2025-07/001593_time_stepping_algorithms_for_parabolic_partial_differential_equations.pdf | |
| Subject | Differential equations, Parabolic -- Dissertations | |
| Subject | Differential equations, Partial -- Dissertations | |
| Title | Time stepping algorithms for parabolic partial differential equations | |
| Type | Master's Thesis | |
| College | College of Science | |
| Department | Mathematics |
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