Skip to main content

plotting - How to integrate numerically the product of result of NDsolve?



I am going to integrate the product of the results of NDsolve, in fact If x and y are the results as interpolating function, How I can integrate x*y numerically?


Table[{Exp[Integrate[ x[t] /. s, {t, 0, i}]]}, {i, -17.5, 10, 1}]

This line does not work for products of x[t]*y[t] or x[t]^2.


This is my entire code file:


yy = {10^-4}; rr = {0.999}; xx = {10^-15}; zz = {10^-4}; mm = {10^-4};


yy + rr + xx^2 + zz - mm^2 - zz^2/24 ic = -17.5

s = NDSolve[{D[y[t],
t] == (3 y[t])/5 - (12 m[t]^2 y[t])/5 + (2 r[t] y[t])/
5 - (6 x[t]^2 y[t])/5 + (3 y[t]^2)/5 + (7 y[t] z[t])/
5 - (y[t] z[t]^2)/10,
D[r[t], t] == -((2 r[t])/5) - (12 m[t]^2 r[t])/5 + (2 r[t]^2)/
5 - (6 r[t] x[t]^2)/5 + (3 r[t] y[t])/5 + (7 r[t] z[t])/
5 - (r[t] z[t]^2)/10,

D[x[t], t] == (9 x[t])/5 - (6 m[t]^2 x[t])/5 + (r[t] x[t])/
5 - (3 x[t]^3)/5 + (3 x[t] y[t])/10 + (x[t] z[t])/
5 - (x[t] z[t]^2)/20,
D[z[t], t] ==
12/5 + (12 m[t]^2)/5 - (12 r[t])/5 - (24 x[t]^2)/5 - (18 y[t])/
5 - (18 z[t])/5 - (6 m[t]^2 z[t])/5 + (r[t] z[t])/
5 - (3 x[t]^2 z[t])/5 + (3 y[t] z[t])/10 + (13 z[t]^2)/10 -
z[t]^3/20,
D[m[t], t] == -2 Sqrt[3] - (6 m[t])/5 -
2 Sqrt[3] m[t]^2 - (6 m[t]^3)/5 +

2 Sqrt[3] r[t] + (m[t] r[t])/5 +
2 Sqrt[3] x[t]^2 - (3 m[t] x[t]^2)/5 +
2 Sqrt[3] y[t] + (3 m[t] y[t])/10 +
2 Sqrt[3] z[t] + (6 m[t] z[t])/5 -
z[t]^2/(4 Sqrt[3]) - (m[t] z[t]^2)/20, x[ic] == xx, y[ic] == yy,
m[ic] == mm, z[ic] == zz, r[ic] == rr}, {x, y^2, z, m, r}, {t, ic,
10}]

Table[{Exp[Integrate[x[t] /. s, {t, 0, i}]]}, {i, -17.5, 10, 1}]


Comments

Popular posts from this blog

plotting - How to draw lines between specified dots on ListPlot?

I would like to create a plot where I have unconnected dots and some connected. So far, I have figured out how to draw the dots. My code is the following: ListPlot[{{1, 1}, {2, 2}, {3, 3}, {4, 4}, {1, 4}, {2, 5}, {3, 6}, {4, 7}, {1, 7}, {2, 8}, {3, 9}, {4, 10}, {1, 10}, {2, 11}, {3, 12}, {4,13}, {2.5, 7}}, Ticks -> {{1, 2, 3, 4}, None}, AxesStyle -> Thin, TicksStyle -> Directive[Black, Bold, 12], Mesh -> Full] I have thought using ListLinePlot command, but I don't know how to specify to the command to draw only selected lines between the dots. Do have any suggestions/hints on how to do that? Thank you. Answer One possibility would be to use Epilog with Line : ListPlot[ {{1, 1}, {2, 2}, {3, 3}, {4, 4}, {1, 4}, {2, 5}, {3, 6}, {4, 7}, {1, 7}, {2, 8}, {3, 9}, {4, 10}, {1, 10}, {2, 11}, {3, 12}, {4, 13}, {2.5, 7}}, Ticks -> {{1, 2, 3, 4}, None}, AxesStyle -> Thin, TicksStyle -> Directive[Black, Bold, 12], Mesh -> Full, Epilog -> { Line[ ...

dynamic - How can I make a clickable ArrayPlot that returns input?

I would like to create a dynamic ArrayPlot so that the rectangles, when clicked, provide the input. Can I use ArrayPlot for this? Or is there something else I should have to use? Answer ArrayPlot is much more than just a simple array like Grid : it represents a ranged 2D dataset, and its visualization can be finetuned by options like DataReversed and DataRange . These features make it quite complicated to reproduce the same layout and order with Grid . Here I offer AnnotatedArrayPlot which comes in handy when your dataset is more than just a flat 2D array. The dynamic interface allows highlighting individual cells and possibly interacting with them. AnnotatedArrayPlot works the same way as ArrayPlot and accepts the same options plus Enabled , HighlightCoordinates , HighlightStyle and HighlightElementFunction . data = {{Missing["HasSomeMoreData"], GrayLevel[ 1], {RGBColor[0, 1, 1], RGBColor[0, 0, 1], GrayLevel[1]}, RGBColor[0, 1, 0]}, {GrayLevel[0], GrayLevel...

list manipulation - Selecting multiple columns from a matrix?

Sample data: data = { {{2013, 1, 1}, 24.13, 167.67, 231.82}, {{2013, 1, 2}, 32.15, 170.92, 225.99}, {{2013, 1, 3}, 35.43, 172.68, 221.67}, {{2013, 1, 4}, 36.73, 173.05, 218.32}, {{2013, 1, 5}, 58.19, 165.96, 197.05}, {{2013, 1, 6}, 69.99, 163.50, 187.52}, {{2013, 1, 7}, 71.37, 154.21, 175.58}, {{2013, 1, 8}, 72.51, 149.66, 163.25}}; I want a DateListPlot with three graphs, so for a matrix formed by columns 1 and 2, one for columns 1 and 3, and 1 for columns 1 and 4. At the moment I'm using this code: data2 = Transpose[{data[[All, 1]], data[[All, 2]]}]; data3 = Transpose[{data[[All, 1]], data[[All, 3]]}]; data4 = Transpose[{data[[All, 1]], data[[All, 4]]}]; DateListPlot[{data2, data3, data4}, Joined -> True, Filling -> {3 -> {1}}] but I have a hunch that this can be done more efficiently. I don't like the Transpose s in particular. Any ideas? edit (for extra credit) What if I need to multiply the second column by 2, which in my solution is simp...