# How can I get a list of solution points from NDSolve?

I just need a list of numerical solutions for x[t], x'[t], x''[t]. While I know how to graph them, I have no idea how to get solutions into a table. Can someone please help?

g = 9.81;
v = 20;
θ = Pi/4;
k1 = 0.2;

sol1 =
NDSolve[
{x''[t] == -k1 x'[t]  Sqrt[y'[t]^2 + x'[t]^2],
y''[t] == -k1  y'[t]  Sqrt[y'[t]^2 + x'[t]^2] - g m,
x[0] == 0, y[0] == 0, x'[0] == v Cos[θ], y'[0] == v Sin[θ]},
{x, y}, {t,0, 10}];

tkoncni = t /. FindRoot[y[t] /. sol1, {t, 1}];

gr11 =
Plot[y[t] /. sol1, {t, 0, tkoncni},
PlotRange -> Automatic, AxesLabel -> {"t", "y(t)"}];

gr12 =
ParametricPlot[{x[t] /. sol1[[1]], y[t] /. sol1}, {t, 0, tkoncni},
PlotRange -> Automatic, AxesLabel -> {"x(t)", "y(t)"}];

• can't you use Table or so?
– Wjx
Commented Jul 7, 2016 at 8:27
• i know i have to use table, i just dont know how to use it correctly Commented Jul 7, 2016 at 10:21

The easy way to do it IMO is to extract the interpolating functions from your solution.

g = 9.81;
v = 20;
θ = Pi/4;
k1 = 0.2;
m = 1.;

sol1 =
NDSolve[
{x''[t] == -k1 x'[t] Sqrt[y'[t]^2 + x'[t]^2],
y''[t] == -k1 y'[t] Sqrt[y'[t]^2 + x'[t]^2] - g m,
x[0] == 0, y[0] == 0, x'[0] == v Cos[θ], y'[0] == v Sin[θ]},
{x, y}, {t, 0, 10}]

{xF, yF} = sol1[[1, All, 2]];
tmax = t /. FindRoot[yF[t], {t, 1}]


1.58915

Table[{xF[t], xF'[t], xF''[t]}, {t, Subdivide[tmax, 10]}]

{{0., 14.1421, -56.5685}, {1.74666, 8.75671, -20.1819},
{2.93728, 6.49064, -10.0301}, {3.8629, 5.26585, -5.92728},
{4.63437, 4.49283, -4.04329}, {5.30152, 3.92479, -3.23141},
{5.88598, 3.43832, -2.9428}, {6.39581, 2.9813, -2.81483},
{6.83461, 2.54532, -2.66073}, {7.20639, 2.13967, -2.43278},
{7.51685, 1.77504, -2.14991}}

Table[{yF[t], yF'[t], yF''[t]}, {t, Subdivide[tmax, 10]}]

{{0., 14.1421, -66.3785}, {1.64027, 7.49102, -27.0749},
{2.54638,   4.19187, -16.2878}, {3.02848, 1.98633, -12.0458},
{3.2019, 0.248938, -10.034}, {3.12038, -1.24218, -8.78726},
{2.8168, -2.54778, -7.62941}, {2.32084, -3.66031, -6.35408},
{1.6645, -4.56506, -5.03796}, {0.880709, -5.26691, -3.82158},
{-4.16334*10^-16, -5.78996, -2.79726}}