NDSolve: What is the solution to the error ???

• To: mathgroup at smc.vnet.net
• Subject: [mg31670] NDSolve: What is the solution to the error ???
• From: fannews at email.com (Steve)
• Date: Fri, 23 Nov 2001 05:47:07 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Hi there,

Would appreciate if someone could help me find the solution to the
error of:
NDSolve::ndnum: Encountered non-numerical value for a
derivative at T== 0.`.

You will face division by error due to the initial conditions, but is
there anything I can do if I want the initial conditions = 0 ??
If nothing can be done, its ok for non-zero initial conditions.
But how to solve the above error??

This may be a silly mistake that I made somewhere, but I can't seem to
find it ....

Here is the code, copy & paste below to Mathematica:

\!\(\*
RowBox[{"NDSolve", "[",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{

RowBox[{\(4\ Cos[\[CapitalLambda]\_3[T]]\),
"-", \(\(484\ a\_1[T]\)\/483\),
"+", \(\(114081221\ a\_1[T]\^3\)\/150238116\),
"-", \(Sin[\[CapitalPhi]\_3[T]]\ a\_2[T]\),
"+", \(484\/161\ a\_1[T]\ a\_2[T]\^2\),
"+", \(242\/161\ Cos[2\ \[CapitalPhi]\_3[T]]\ a\_1[
T]\ a\_2[T]\^2\),
"+", \(Cos[\[CapitalPhi]\_3[
T]]\ \((a\_2[
T] - \(234256\ a\_1[T]\^2\ a\_2[T]\)\/77763 -
3\/2\ a\_2[T]\^3)\)\), "+",
RowBox[{"22", " ", \(a\_1[T]\), " ",
RowBox[{"(",
RowBox[{\(34\/3\), "-",
RowBox[{
SubsuperscriptBox["\[CapitalLambda]", "3",
"\[Prime]",
MultilineFunction->None], "[", "T", "]"}]}],
")"}]}]}], "==", "0"}], ",",
RowBox[{

RowBox[{\(4\ Sin[\[CapitalLambda]\_3[T]]\),
"-", \(\(15961\ a\_1[T]\)\/483\),
"+", \(Cos[\[CapitalPhi]\_3]\ a\_2[T]\),
"+", \(242\/161\ Sin[2\ \[CapitalPhi]\_3[T]]\ a\_1[
T]\ a\_2[T]\^2\),
"+", \(Sin[\[CapitalPhi]\_3[
T]]\ \((a\_2[
T] - \(234256\ a\_1[T]\^2\ a\_2[T]\)\/77763 -
3\/2\ a\_2[T]\^3)\)\), "-",
RowBox[{"22", " ",
RowBox[{
SubsuperscriptBox["a", "1", "\[Prime]",
MultilineFunction->None], "[", "T", "]"}]}]}],
"==",
"0"}], ",",
RowBox[{

RowBox[{\(\(117128\ a\_1[T]\^2\ a\_2[T]\)\/25921\),
"+", \(\(239936708\ Cos[
2\ \[CapitalPhi]\_3[T]]\ a\_1[T]\^2\ a\_2[
T]\)\/106146495\), "+", \(9\/4\ a\_2[T]\^3\),
"+",
RowBox[{\(Sin[\[CapitalPhi]\_3[T]]\), " ",
RowBox[{"(",
RowBox[{\(\(5324\ a\_1[T]\)\/161\), "+",
RowBox[{\(22\/483\), " ",
RowBox[{
SubsuperscriptBox["a", "1", "\[Prime]",
MultilineFunction->None], "[", "T",
"]"}]}]}],
")"}]}], "+",
RowBox[{\(Cos[\[CapitalPhi]\_3[T]]\), " ",
RowBox[{"(",

RowBox[{\(-\(\(28344976\ a\_1[T]\^3\)\/12519843\)\),

"-", \(726\/161\ a\_1[T]\ a\_2[T]\^2\), "-",
RowBox[{\(22\/483\), " ", \(a\_1[T]\), " ",
RowBox[{"(",
RowBox[{\(34\/3\), "-",
RowBox[{

SubsuperscriptBox["\[CapitalLambda]", "3",

"\[Prime]",
MultilineFunction->None], "[", "T",
"]"}]}],
")"}]}]}], ")"}]}], "+",
RowBox[{\(a\_2[T]\), " ",
RowBox[{"(",
RowBox[{\(97\/3\), "-",
RowBox[{
SubsuperscriptBox["\[CapitalLambda]", "3",
"\[Prime]",
MultilineFunction->None], "[", "T", "]"}],
"+",
RowBox[{
SubsuperscriptBox["\[CapitalPhi]", "3",
"\[Prime]",
MultilineFunction->None], "[", "T", "]"}]}],
")"}]}]}], "==", "0"}], ",",
RowBox[{

RowBox[{\(\(-\(3\/2\)\)\ a\_2[T]\),
"-", \(\(239936708\ Sin[
2\ \[CapitalPhi]\_3[T]]\ a\_1[T]\^2\ a\_2[
T]\)\/106146495\), "+",
RowBox[{\(Cos[\[CapitalPhi]\_3[T]]\), " ",
RowBox[{"(",
RowBox[{\(\(5324\ a\_1[T]\)\/161\), "+",
RowBox[{\(22\/483\), " ",
RowBox[{
SubsuperscriptBox["a", "1", "\[Prime]",
MultilineFunction->None], "[", "T",
"]"}]}]}],
")"}]}], "-",
RowBox[{
SubsuperscriptBox["a", "2", "\[Prime]",
MultilineFunction->None], "[", "T", "]"}], "-",
RowBox[{\(Sin[\[CapitalPhi]\_3[T]]\), " ",
RowBox[{"(",

RowBox[{\(-\(\(28344976\ a\_1[T]\^3\)\/12519843\)\),

"-", \(726\/161\ a\_1[T]\ a\_2[T]\^2\), "-",
RowBox[{\(22\/483\), " ", \(a\_1[T]\), " ",
RowBox[{"(",
RowBox[{\(34\/3\), "-",
RowBox[{

SubsuperscriptBox["\[CapitalLambda]", "3",

"\[Prime]",
MultilineFunction->None], "[", "T",
"]"}]}],
")"}]}]}], ")"}]}]}], "==", "0"}],
",", \(a\_1[0] == 0\), ",", \(a\_2[0] == 0\),
",", \(\[CapitalLambda]\_3[0] == 0\),
",", \(\[CapitalPhi]\_3[0] == 0\)}], "}"}],
",", \({a\_1, a\_2, \[CapitalLambda]\_3, \[CapitalPhi]\_3}\),
",", \({T, 0, 10}\), ",",
RowBox[{"MaxSteps", "->",
InterpretationBox["\[Infinity]",
DirectedInfinity[ 1]]}], ",", \(Method -> RungeKutta\),
",", \(WorkingPrecision -> 16\)}], "]"}]\)

```

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