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NDSolve::ivres

NDSolve::ivres

Details

  • This message occurs when NDSolve is unable to get an consistent set of initial conditions for a general differential algebraic equation written in residual form .
  • The message is issued when the specified initial conditions are found to be inconsistent with the underlying DAE system.
  • The message warns that the specified initial conditions have been modified to generate a consistent set of initial conditions.
  • Off[message] switches off the message; On[message] switches it on. For example: Off[NDSolve::ivres].

Examples

Basic Examples  (1)

For the single-pendulum problem, the initial condition is inconsistent with the algebraic equation since has to evaluate to a real-valued number:

Wolfram Language code: eqns = {x'[t] == xp[t], xp'[t] == λ[t] x[t], y'[t] == yp[t], yp'[t] == λ[t] y[t] - 1, x[t] ^ 2 + y[t] ^ 2 == 1}; ics = {x[0] == 2, yp[0] == 1}; res = NDSolve[{eqns, ics}, {x, xp, y, yp, λ}, {t, 0, 5}, Method -> "IndexReduction" -> True]

Both the initial conditions are modified to ensure consistent initial conditions:

Wolfram Language code: {x[0], yp[0]} /. res[[1]]

Provide consistent initial conditions to resolve the issue:

Wolfram Language code: eqns = {x'[t] == xp[t], xp'[t] == λ[t] x[t], y'[t] == yp[t], yp'[t] == λ[t] y[t] - 1, x[t] ^ 2 + y[t] ^ 2 == 1}; ics = {x[0] == 1, yp[0] == 1}; NDSolve[{eqns, ics}, {x, xp, y, yp, λ}, {t, 0, 5}, Method -> "IndexReduction" -> True]