Title: Convergence of theta-method for time-variable equations Associated People:
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Bibliographic record
Abstract
If a vector is obtained by a repetitive matrix iteration, then it tends to zero, once the maximal by the absolute value eigenvalue of the matrix is inside the unit circle. This is not true anymore for a sequence of variable matrices. The recently published paper by University of Calgary mathematician Elena Braverman, together with the exchange PhD student from Turkey Ba\\c{s}ak Karpuz, considers the stability problem when some of the iteration matrices may have large eigenvalues. The original problem which is a high order difference equation can also include nonlinearities. Sufficient stability conditions are obtained and applied to the analysis of the theta finite difference scheme which is the simplest semi-implicit generalization of the Euler method. Depending on the values of the parameter h which describes the step size, scalar solutions can converge to zero in a monotone or oscillatory way, or diverge.
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Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.008 | 0.001 |
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