i want to solve this equation and plot it solution w.r.t N2 and theta(0)
theta''[x] + 2*theta'[x] -
Exp[-2*x]*(N2)^2*(theta[x] - 5) + Q1 == 0
anyone please help
$\begingroup$
$\endgroup$
2
1 Answer
$\begingroup$
$\endgroup$
5
It is not clear what you want plotted nor how you want the plots done. Neither have you specified the range of the variables that are of interest. The following will need to be tailored once you understand your needs.
Clear["Global`*"]
{xmin, xmax} = {0, 1};
Manipulate[
Module[{eqns1, sol1},
eqns1 =
{theta''[x] + 2*theta'[x] - Exp[-2*x]*N21^2*(theta[x] - 5) + Q11 == 0,
theta[0] == t01, theta'[0] == tp01};
sol1 = ParametricNDSolve[eqns1, theta, {x, xmin, xmax}, N21];
Plot3D[Evaluate[theta[N21][x] /. sol1],
{x, xmin, xmax}, {N21, 0, 5},
AxesLabel -> (Style[#, 14, Bold] & /@ {"x", "N2", "theta"}),
ClippingStyle -> None]],
{{Q11, 5, Q1}, 0, 10, Appearance -> "Labeled"},
{{t01, 0, "theta[0]"}, 0, 10, Appearance -> "Labeled"},
{{tp01, 0, "theta'[0]"}, 0, 10, Appearance -> "Labeled"}]
(* spacer *)
Manipulate[
Module[{eqns2, sol2},
eqns2 =
{theta''[x] + 2*theta'[x] - Exp[-2*x]*N22^2*(theta[x] - 5) + Q12 == 0,
theta[0] == t02, theta'[0] == tp02};
sol2 = ParametricNDSolve[eqns2, theta, {x, xmin, xmax}, t02];
Plot3D[Evaluate[theta[t02][x] /. sol2],
{x, xmin, xmax}, {t02, 0, 5},
AxesLabel -> (Style[#, 14, Bold] & /@ {"x", "theta[0]", "theta"}),
ClippingStyle -> None]],
{{Q12, 5, Q1}, 0, 10, Appearance -> "Labeled"},
{{N22, 5, N2}, 0, 10, Appearance -> "Labeled"},
{{tp02, 0, "theta'[0]"}, 0, 10, Appearance -> "Labeled"}]
(* spacer *)
answered Jan 6, 2019 at 17:50
-
$\begingroup$ thanks a lot, I want to get a two-dimensional plot with N2 on X-axis and theta(0) on y axis $\endgroup$– ZDNCommented Jan 7, 2019 at 7:42
-
$\begingroup$ @ziauddin - so what are the ranges of interest or values for
Q1andxand the range of interest fortheta[0]? $\endgroup$ Commented Jan 7, 2019 at 13:10 -
$\begingroup$ Q1 may be any constant, theta(0) may be from 0-1 and N2 from 0-10 $\endgroup$– ZDNCommented Jan 7, 2019 at 16:03
-
$\begingroup$ You still have not specified the range for
x$\endgroup$ Commented Jan 7, 2019 at 16:17 -
DSolvein the documentation $\endgroup$ParametricNDSolve(with capitalPat the beginning) seems to be relevant. $\endgroup$