StiffnessSwitching

Introduction

The basic idea behind the StiffnessSwitching method is to provide an automatic means of switching between a nonstiff and a stiff solver.

The StiffnessTest option (described within StiffnessTest) provides a useful means of detecting when a problem appears to be stiff.

The StiffnessSwitching method traps any failure code generated by StiffnessTest and switches to an alternative solver.

Extrapolation provides a powerful technique for computing highly accurate solutions using dynamic order and step size selection (see Extrapolation for more details) and are therefore used as the default choice in StiffnessSwitching.

Examples

This loads some useful packages.

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This selects a stiff problem and specifies a longer integration time interval than the default specified by NDSolveProblem.

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The default Extrapolation base method is not appropriate for stiff problems and gives up quite quickly.

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Instead of giving up, the StiffnessSwitching method continues the integration with a stiff solver.

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The StiffnessSwitching method uses a pair of extrapolation methods as the default. The nonstiff solver uses the ExplicitModifiedMidpoint base method, and the stiff solver uses the LinearlyImplicitEuler base method.

For small values of the AccuracyGoal and PrecisionGoal tolerances, it is sometimes be preferable to use an explicit Runge-Kutta method for the nonstiff solver.

The ExplicitRungeKutta method eventually gives up when the problem is considered to be stiff.

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This sets the ExplicitRungeKutta method as a submethod of StiffnessSwitching.

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A switch to the stiff solver occurs at and a plot of the step sizes used shows that the stiff solver takes much larger steps.

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Option summary