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MathGroup Archive 2001

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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 ....

Many Thanks in advance :)


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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