| | Apart from solving initial value problems, for which the integrator is a key component of a simulator, integrators can also be used to solve boundary value problems (via numerical methods like the Multiple Shooting Method) and trajectory optimization problems (via numerical methods like direct transcription). IntegratorBase and its derivatives were developed primarily toward the former application (through IntegratorBase::IntegrateNoFurtherThanTime() and the Simulator class). However, the IntegratorBase architecture was developed to support these ancillary applications as well using the IntegratorBase::IntegrateWithMultipleStepsToTime() and IntegratorBase::IntegrateWithSingleFixedStepToTime() methods; the latter permits the caller to advance time using fixed steps in applications where variable stepping would be deleterious (e.g., direct transcription).
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