Dear Maple users

Some ODE's like the Lotka Volterra system can only be solved numerically. I would like to solve some equations based on the numerical solution to that system. Let the x(t) and y(t) be the solutions to the ODE system. 

Now, obviously it won't work afterwards to write an equation like solve(x(t)=60,t), since the solution of the ODE only exists as a procedure. Of course I can make an odeplot and zoom in to get an approximate solution to x(t)=60. I would however like it to done automatically. How is this done in the most convenient way when the soltuion of the ODE is given as a procedure?

Example attached. 

Regards

Erik

Lotka_Volterra.mw

Dear Maple users

I am trying to test how well data from a real throw with a ball comply with the usual model, in which the air resistance is proportional to the square of the velocity. I succeeded in solving the ODE system numericallly using the rkf45 method and plottet the solutioncurve (see attached file). I am however unsure how I can retrieve the data from the model in the most convenient way in order to compare them to the data from the real throw. The latter I have as (t, x(t), y(t)) data in three columns in an Excel file. Of course I can import the x og y columns into Maple and create a plot containing both the (x,y) data from Excel and the (x,y) data from the model. The problem is however that even if the (x,y) curves are rather close, if may not be a good model. I need to take into account the time variabel as well! The data from the Excel file contains data for every 1/30 second. What I like is to be able to compute the Root Mean Square of all (x_experiment(t)-x_model(t), y_experiment(t)-y_model(t)) data - or would the Root Mean Square of the (Euclid) distances between the points be better?

Now back to my question on how to retrieve data from the ODE system in the most convenient way. I have read the help page for the dsolve command. There is however several options, that I am unsure about, for example the output option (listprocedure, etc). I hope someone can help. 

NB! Excel data are imported column by column into Maple as n x 1 matrices.

Regards,

Erik V. 

Throw_with_air_resistance_1.mw
 

Dear Maple users

I have been investigating the one-dimensional Wave Equation for the vibrating string with fixed endpoints. Before trying to use Maple for a solution, I surfed on Google and stumbled upon a solution given in a GeoGebra animation:

https://www.geogebra.org/m/eKkFV8uz

I succeded in making a similar animation in Maple. See the attached Maple file: The last line is out-commented in order for the file not to be too big (saving many frames...). Remove the # and recalculate, select the animation object and eventually resize it. Then hit the Play Button in the Toolbar. It should work very much like the animation above. 

Now my question: I assume the numerical solution is solved using the Finite Difference Scheme in the background? How do I receive the numerical data, which lies behind the animation? Is it possible to evaluate the solution at specific (x,t) points?

I am quite impressed that GeoGebra can solve this PDE, by the way!

Regards,

Erik

Wave_Equation_-_vibrating_string2.mw

Dear Maple users

I have a possibly quite easy question: How do I calculate or refer to a partial derivative evaluated at some specific point? The Maple documentation was no help to me in this regard. I hope the picture below indicate what I am looking for. I am using Maple 2D notation, but not excited about using the vertical line as evaluation. What ways can it be accomplished?

Erik

Dear Maple users

Let's say I want to plot a line containing a parameter, for example (a+2)*x+6, where a is the parameter. When using the following Explore command:

Explore(plot((a+2)*x+6, x = -5 .. 5, view = -10 .. 10), parameters = [a = -4.0 .. 3], initialvalues = [a = 1])

I will be able to change the value of a by using the slider. The actual value of a is currently displayed as well. Now, However, I want to have the current value of the slope of the line displayed as I move the slider. How is this done? When using a print command inside the Explore command the value of a+2 is not displayed, rather "a+2". Can I use some kind of component?

I hope someone can help. 

NB! I constructed this rather doll example, just to make it simple.

Regards, Erik