3
$\begingroup$
ClearAll[n, c, w1, w2, x, y, g, p1, p2, p3, p4, Eq1, Eq2, sol]

n = 1;

w1 = -(1/3) - 2*(Sqrt[g[x]]*Sqrt[1 - g[x]/y[x]])/3;

w2 = (0.2)*(1 + y[x])^n/(g[x])^(n - 1)*(1 - g[x] + y[x]);

Eq1 = g'[x] == -3*g[x]*(1 - g[x] + y[x])*(w1 - w2) + 
    y[x]*g[x]*(1 + 3*w1);

Eq2 = y'[x] == -3*y[x]*(1 - g[x] + y[x])*(w1 - w2) + 
    y[x]*(1 + y[x])*(1 + 3*w1);

sol = NDSolve[{Eq1, Eq2, g[0] == 0.72, y[0] == 0.08}, {g, y}, {x, -10,
     10}, AccuracyGoal -> 2];

p1 = Plot[{Evaluate[{g[x],y[x]} /. sol]}, {x, -10, 10}];

when I try to solve equations the graphs are empty, how can I solve that?

$\endgroup$
3
  • 1
    $\begingroup$ Remove MaxSteps -> 500 $\endgroup$
    – Chris K
    Commented Feb 13, 2017 at 17:44
  • $\begingroup$ ok. why my graphs are empty, it is not plotting $\endgroup$
    – merve
    Commented Feb 13, 2017 at 17:49
  • 2
    $\begingroup$ At x==0, g'[x] and y'[x] are complex-valued ({Eq1, Eq2} /. {g[x] -> 0.72, y[x] -> 0.08} gives {Derivative[1][g][x] == 0.319666 + 0.96768 I, Derivative[1][y][x] == 0.0355185 - 0.27648 I}). Is that what you expect? I notice you changed the definition of w1 in your edit. $\endgroup$
    – Chris K
    Commented Feb 13, 2017 at 18:16

1 Answer 1

2
$\begingroup$

Real Part

ClearAll[n, w1, w2, p1, sol]

n = 1;

w1[x_] := Re[-(1/3) - 2*(Sqrt[g[x]]*Sqrt[1 - g[x]/y[x]])/3];

w2[x_] := Re[(1/5)*(1 + y[x])^n/(g[x])^(n - 1)*(1 - g[x] + y[x])];

sol = NDSolve[{
    g'[x] == -3*g[x]*(1 - g[x] + y[x])*(w1[x] - w2[x]) + y[x]*g[x]*(1 + 3*w1[x]),
    y'[x] == -3*y[x]*(1 - g[x] + y[x])*(w1[x] - w2[x]) + y[x]*(1 + y[x])*(1 + 3*w1[x]),
    g[0] == 0.72, y[0] == 0.08},
   {g, y}, {x, -10, 10}];

p1 = Plot[{Evaluate[{g[x], y[x]} /. sol]}, {x, -10, 10}, 
  PlotStyle -> {Blue, Red}, Axes -> None, Frame -> True]

p2 = Plot[{Evaluate[w1[x] /. sol], Evaluate[w2[x] /. sol]}, {x, -10, 10},
  PlotStyle -> {Blue, Red}, PlotRange -> Full, Axes -> None, Frame -> True]

enter image description here

enter image description here

Imaginary Part

w1[x_] := Im[-(1/3) - 2*(Sqrt[g[x]]*Sqrt[1 - g[x]/y[x]])/3];

w2[x_] := Im[(1/5)*(1 + y[x])^n/(g[x])^(n - 1)*(1 - g[x] + y[x])];
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.