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The integration to steady state of many initial value ODEs and PDEs using the forward Euler method
can alternatively be considered as gradient descent for an associated minimization problem.
Greedy algorithms such as steepest descent for determining the step size are as
slow to reach steady state as is forward Euler integration with the best uniform step size.
But other, much faster methods using bolder step size selection exist.
Various alternatives are investigated from both theoretical and practical...
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