Creating NDSolve`StateData Objects

ProcessEquations

The first stage of any solution using NDSolve is processing the equations specified into a form that can be efficiently accessed by the actual integration algorithms. This stage minimally involves determining the differential order of each variable, making substitutions needed to get a first-order system, solving for the time derivatives of the functions in terms of the functions, and forming the result into a NumericalFunction object. If you want to save the time of repeating this process for the same set of equations or if you want more control over the numerical integration process, the processing stage can be executed separately with NDSolve`ProcessEquations.

This creates a list of two NDSolve`StateData objects because there are two possible solutions for the y' in terms of y.

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Reinitialize

It is not uncommon that the solution to a more sophisticated problem involves solving the same differential equation repeatedly, but with different initial conditions. In some cases, processing equations may be as time-consuming as numerically integrating the differential equations. In these situations, it is a significant advantage to be able to simply give new initial values.

Reusing processed equations.

This creates an NDSolve`StateData object for the harmonic oscillator.

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This creates three new NDSolve`StateData objects, each with a different initial condition.

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Using NDSolve`Reinitialize may save computation time when you need to solve the same differential equation for many different initial conditions, as you might in a shooting method for boundary value problems.