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NDSolve::index NDSolveValue::index ParametricNDSolve::index ParametricNDSolveValue::index

NDSolve::index NDSolveValue::index ParametricNDSolve::index ParametricNDSolveValue::index

Details

  • Currently, NDSolve can integrate differential algebraic equations that are index 1 or less. NDSolve performs structural analysis to determine the index of the system and issues this message if the index of the system is greater than 1.
  • Off[message] switches off the message; On[message] switches it on. For example: Off[NDSolve::index].

Examples

Basic Examples  (1)

The differential algebraic equation system is an index-3 system that cannot be solved without performing index reduction:

Wolfram Language code: NDSolve[{x'[t] + y[t] == 0, y'[t] + z[t] == 0, z'[t] + w[t] == 0, y[t] == Sin[t], x[0] == 1}, {x, y, z}, {t, 0, 1}]

Differentiating the last equation and substituting into the second equation gives . Differentiating again and substituting the third equation gives . Differentiating again gives the final system. Since the DAE was differentiated three times, the index is said to be 3:

Wolfram Language code: NDSolve[{x'[t] + y[t] == 0, y'[t] + z[t] == 0, z'[t] + w[t] == 0, y[t] == Sin[t], x[0] == 1}, {x, y, z}, {t, 0, 1}, Method -> {"IndexReduction" -> True}]