FixedStep Method for NDSolve
Introduction
It is often useful to carry out a numerical integration using fixed step sizes.
For example, certain methods such as
DoubleStep and
Extrapolation carry out a sequence of fixed-step integrations before combining the solutions to obtain a more accurate method with an error estimate that allows adaptive step sizes to be taken.
The method
FixedStep allows any one-step integration method to be invoked using fixed step sizes.
This loads a package with some example problems and a package with some utility functions.
Examples
Define an example problem. |
This integrates a differential system using the method ExplicitEuler with a fixed step size of 1/10.
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Actually the ExplicitEuler method has no adaptive step size control. Therefore, the integration is already carried out using fixed step sizes so the specification of FixedStep is unnecessary.
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Here are the step sizes taken by the method ExplicitRungeKutta for this problem.
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This specifies that fixed step sizes should be used for the method ExplicitRungeKutta.
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The option
MaxStepFraction provides an absolute bound on the step size that depends on the integration interval.
Since the default value of MaxStepFraction is 1/10, the step size in this example is bounded by one-tenth of the integration interval, which leads to using a constant step size of 1/20.
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By setting the value of MaxStepFraction to a different value, the dependence of the step size on the integration interval can be relaxed or removed entirely.
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Option summary
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| Method | None | specify the method to use with fixed step sizes. |
Option of the method FixedStep.
