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NDSolve::ndcf NDSolveValue::ndcf ParametricNDSolve::ndcf ParametricNDSolveValue::ndcf

NDSolve::ndcf NDSolveValue::ndcf ParametricNDSolve::ndcf ParametricNDSolveValue::ndcf

Details

  • This message is generated by a specific type of failure within the algorithms that are used for computing numerical solutions of ordinary differential equations.
  • If you see this message and the cause is not evident from the nature of the example, please send your example to Technical Support so that it can be investigated.
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Examples

Basic Examples  (2)

Consider the following differential algebraic equation:

Wolfram Language code: eqns = {x''[t] == y[t], y[t] ^ 2 + x[t] ^ 2 == 1, x[0] == 1, x'[0] == 0}; NDSolve[eqns, {x, y}, {t, 0, 1}]

The problem is with the initial conditions. says that from the second equation. says that . Thus, the pendulum has no initial velocity or acceleration, so it just sits there, which causes the problem. Changing the initial conditions helps:

Wolfram Language code: eqns2 = {x''[t] == y[t], y[t] ^ 2 + x[t] ^ 2 == 1, x[0] == 0.5, x'[0] == 0}; NDSolve[eqns2, {x, y}, {t, 0, 1}]

Note that the index reduction methods also have a problem with the original initial conditions:

Wolfram Language code: eqns = {x''[t] == y[t], y[t] ^ 2 + x[t] ^ 2 == 1, x[0] == 1, x'[0] == 0}; NDSolve[eqns, {x, y}, {t, 0, 1}, Method -> {"IndexReduction" -> "Pantelides"}]; NDSolve[eqns, {x, y}, {t, 0, 1}, Method -> {"IndexReduction" -> "StructuralMatrix"}];

Finding solutions of differential equations with discontinuities can be problematic, and increasing the working precision may not be a solution:

Wolfram Language code: eqns = {Derivative[1][p][t] == 4. (-0.005 Sqrt[-100. + p[t]^2] + 0.07 Sqrt[600.  - p[t]] z[t]), Derivative[1][z][t] == (Piecewise[ {{Max[0, 0.4*(170. - p[t]) - 1.2*(-0.005*Sqrt[-100. + p[t]^2] + 0.07*Sqrt[600. - p[t]]*z[t])], z[t] <= 0}, {Min[0, 0.4*(170. - p[t]) - 1.2*(-0.005*Sqrt[-100. + p[t]^2] + 0.07*Sqrt[600. - p[t]]*z[t])], z[t] >= 1}}, 0.4*(170. - p[t]) - 1.2*(-0.005*Sqrt[-100. + p[t]^2] + 0.07*Sqrt[600. - p[t]]*z[t])]), p[0] == 140., z[0] == 0.5}; newEqns = Map[Rationalize[#, 0]&, eqns]; NDSolve[newEqns, {p, z}, {t, 0, 20}, WorkingPrecision -> 100];

The Piecewise function is problematic. Use "DiscontinuityProcessing"False:

Wolfram Language code: NDSolve[newEqns, {p, z}, {t, 0, 20}, Method -> {"DiscontinuityProcessing" -> False}]