Parallel Methods and Higher Dimensional NLS Equations
Alternating direction implicit (ADI) schemes are proposed for the solution of the two-dimensional coupled nonlinear Schrödinger equation. These schemes are of second- and fourth-order accuracy in space and second order in time. The resulting schemes in each ADI computation step correspond to a block...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/497439 |
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| Summary: | Alternating direction implicit (ADI) schemes are proposed for the solution of the two-dimensional coupled nonlinear Schrödinger
equation. These schemes are of second- and fourth-order accuracy in space
and second order in time. The resulting schemes in each ADI computation step correspond to a block tridiagonal system which can be solved
by using one-dimensional block tridiagonal algorithm with a considerable
saving in computational time. These schemes are very well suited for parallel implementation on a high performance system with many processors
due to the nature of the computation that involves solving the same block
tridiagonal systems with many right hand sides. Numerical experiments
on one processor system are conducted to demonstrate the efficiency and
accuracy of these schemes by comparing them with the analytic solutions.
The results show that the proposed schemes give highly accurate results. |
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| ISSN: | 1085-3375 1687-0409 |