Plot column using some list as x values?

Question

I've got a mathematica notebook that uses RK4 to successively approximate solutions to a vector valued DE. The output is a nested list similar to:

solutions := {{a[t0],b[t0],c[t0],d[t0]},{a[t0+dt],b[t0+dt],c[t0+dt],d[t0+dt]},...}

The list that I want to use as the x-axis is simply {t0,t0+dt,t0+2dt,...}, and I want to plot it against the a column of my solutions matrix. Perhaps I'm missing it, but I couldn't get ParametricPlot to work with these lists.

Here's a link to my notebook: http://pastebin.com/ZK0pUBSz

Sample data:

t:={0,20,40,60,80,100,120,140,160,180,200}

y:={200.,177.847,162.025,150.607,142.306,136.239,131.788,128.518,126.111,124.341,123.04}

Desired output is a plot with y as the dependent variable and t as the independent variable.

---

(edit: Solved! I had previously defined solutions as a matrix without any argument, and when I tried to turn it into something that took an argument, the kernel threw up errors. Solved by running a simple Remove@solutions.)

An an extra aside, my end goal is to see the effect of step size on solution resolution. I tried to accomplish this using the following code:

Tlist[step_] := 
Transpose[{Range[0, tmax, step], Part[solutions[step], All, 1]}];
ListLinePlot[{TList[.1], Tlist[.5], Tlist[1]}]

I'm trying to create a plot with each step size using Tlist, but the evaluation fails with write protection. Maybe this isn't the right way to tackle this problem in Mathematica, and I'm taking too much of a procedural approach. Any guidance on this would be welcome!

Here's the code for solutions:

RungeKutta[func_List, yinit_List, y_List, step_] := 
 Module[{k1, k2, k3, k4}, 
  k1 = step N[func /. MapThread[Rule, {y, yinit}]];
  k2 = step N[func /. MapThread[Rule, {y, k1/2 + yinit}]];
  k3 = step N[func /. MapThread[Rule, {y, k2/2 + yinit}]];
  k4 = step N[func /. MapThread[Rule, {y, k3 + yinit}]];
  yinit + Total[{k1, 2 k2, 2 k3, k4}]/6]
solutions[step_] := 
 NestList[RungeKutta[func, #, y, step] &, N[yinit], Round[tmax/step]]

RungeKutta code from here: Solving a system of ODEs with the Runge-Kutta method

Answer 1

Suppose xColumn is the column of x-values and yColumn the y-values. Then - as pointed to by YvesKlett - you could use ListPlot[Transpose[{xColumn,yColumn}]], for instance.

In your case:

xColumn=Table[t0+i*dt,{i,0,n}];
yColumn=solutions[[All,1]];

Here, n clearly has to be adjusted to your code, depending on how long your time interval is. Then use for instance the ListPlot command from above with option Joined->True or use ListLinePlot instead.