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", "â?²â?²",
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", "â?²â?²",
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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