| Abstract: |
| Bernstein`s problem asks for the maximum positive real number $R$ for which an absolutely monotonic function, with a specified number of derivatives at the origin, exists on the interval $(-R,0)$. Optimal threshold factors govern the maximum allowable step-size for positivity preserving integration methods of initial-value problems. This talk establishes a link between Bernstein`s problem and optimal threshold factors and presents algorithms for computing the latter. Derivation of optimal exponential integrators of specified accuracy for evolution equations is discussed. |
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