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MathGroup Archive 2006

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system of nonlinear equations in mathematica?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg72273] system of nonlinear equations in mathematica?
  • From: pilly4u <swati_2756 at yahoo.co.in>
  • Date: Sun, 17 Dec 2006 06:20:35 -0500 (EST)
  • Organization: The Math Forum

Hai all,

I am tryign to solve a system of nonlinear differential equations using mathematica.I think there exists singularity in my equations and am new to mathematica and donoy know i to get the problem resolved.Please help me out in this.thought to attach my equations here which i couldnt do.please do reply me through email to saihone at gmail.com.

0.5(derivative(f)+x(derivative(derivative(x))= - derivative(0.1*k^2/d(derivative(derivative(f))));
 
-10(k+0.5*x*derivative(k)) = derivative(0.1*k*k*derivative(k)/d) + 0.1*k^2*(derivative(derivative(f))^2/d - d;

10(-2d-derivative(d)*x/2) = derivative(0.1*k^2*derivative(d)/d) + 0.144*k*(derivative(derivative(f))^2) - 1.92*d^2/k

the code i wrote is 


\!\(\*
  RowBox[{\(eqdiff1 = 10\/2\ \(f\^â?²\)[x] + \(10\/2\) \(xf\^â?³\)[x] == \(f\^3\)[
                    x];\), "\[IndentingNewLine]", 
    RowBox[{
      RowBox[{"eqdiff2", "=", 
        RowBox[{\(\(-10\)*k[x] - 10\/2*\(xk'\)[x]\), "==", 
          RowBox[{
            FractionBox[
              RowBox[{"0.1`", " ", \(k[x]\), 
                SuperscriptBox[
                  RowBox[{
                    SuperscriptBox["k", "â?²",
                      MultilineFunction->None], "[", "x", "]
          "}], "2"]}], \(d[x]\)], "+", 
            FractionBox[
              RowBox[{"0.1`", " ", \(k[x]\^2\), " ", 
                RowBox[{
                  SuperscriptBox["k", "â?²",
                    MultilineFunction->None], "[", "x", "]"}], \(\(d\^â?²\)[
                  x]\)}], \(d[x]\^2\)], "+", 
            FractionBox[
              RowBox[{"0.1`", " ", \(k[x]\^2\), " ", 
                RowBox[{
                  SuperscriptBox["k", "��",
                    MultilineFunction->None], "[", "x", "]"}]}], \(d[x]\)], 
                "+", \(0.1*k[x]^2*\(f''\)[x]^2\/d[x]\), "-", \(d[x]\)}]}]}], 
            ";"}], "\[IndentingNewLine]", 
    RowBox[{
      RowBox[{"eqdiff3", "=", 
        RowBox[{\(2\ 10\ d[x] - \(10\/2\) \(xd\^â?²\)[x]\), "==", 
          RowBox[{
            RowBox[{"-", 
              FractionBox[
                RowBox[{"0.1`", " ", \(k[x]\^2\), " ", 
                  SuperscriptBox[
                    RowBox[{
                      SuperscriptBox["d", "â?²",
              
                      MultilineFunction->None], "[", "
              x", "]"}], "2"]}], \(d[x]\^2\)]}], "+", 
            FractionBox[
              RowBox[{"0.1`", " ", \(k[x]\), " ", 
                RowBox[{
                  SuperscriptBox["d", "â?²",
                    MultilineFunction->None], "[", "x", "]"}], " ", 
                RowBox[{
                  SuperscriptBox["k", "â?²",
            
                MultilineFunction->None], "[", "x", "]"}]}], \(d[x]\)], "+", 
            FractionBox[
              RowBox[{"0.1`", " ", \(k[x]\^2\), " ", 
                RowBox[{
                  SuperscriptBox["d", "��",
                    MultilineFunction->None], "[", "x", "]
                    "}]}], \(d[x]\)], "-", \( .144  k[x] \(f''\)[x]^2\), "+
                  ", \(1.92  d[x]^2\/k[x]\)}]}]}], ";
              "}], "\[IndentingNewLine]", \(sol =
             NDSolve[{eqdiff1, eqdiff2, eqdiff3, \[IndentingNewLine] (*
            Initial\ conditions*) \[IndentingNewLine]k[0] == 1, d[0] == 
          2, \(f'\)[0] == 3, \(d'\)[0] == 0, \(k'\)[0] == 4, \(f''\)[0] == 
3}, \[IndentingNewLine]{k, f, d}, {x, 0,  .4}]\), "\[IndentingNewLine]", 
    RowBox[{"{", 
      RowBox[{"{", 
        RowBox[{
          RowBox[{"k", "->", 
            TagBox[\(InterpolatingFunction[{{0.`, 0.4`}}, "\<<>\>"]\),
              False,
              Editable->False]}], ",", 
          RowBox[{"f", "->", 
            TagBox[\(InterpolatingFunction[{{0.`, 0.4`}}, "\<<>\>"]\),
              False,
              Editable->False]}], ",", 
          RowBox[{"d", "->", 
            TagBox[\(InterpolatingFunction[{{0.`, 0.4`}}, "\<<>\>"]\),
              False,
              Editable->False]}]}], "}"}], "}"}], 
      "\[IndentingNewLine]", \(Plot[Evaluate[{k[x], f[
    x], d[x]} /. sol], {x, 0,  .4}]\)}]\)
Thankyou all,
pilly


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