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Polymath tutorial on Ordinary Differential Equation Solver
The following is the differential equation we want to solve using Polymath
At t=0, ๐ถ๐ = 0.5 and ๐ถ๐ = 0.
and integration time span is t= 0 to t=
First, launch Polymath which you can download from http://www.polymath-software.com. You
will see a window that looks like this.
To use the ODE solver in Polymath, first click on the โProgramโ tab present on the toolbar. This will
bring up a list of options from which you need to select. In this case we need to solve differential
equations so select "DEQ Differential Equations". The shortcut button โdxโ for differential equation
solver is also present on the menu bar ( ) as shown by red circle in below screenshot
This will open up another window, which looks like this.
To enter the differential equations, press the " d(x) +
" button ( ) present on the menu bar
(shown by red circle in the below screenshot). This will bring up a dialogue box in which you can
enter your differential equation. You will also need to specify an initial value for the differential
variable.
In the above dialogue box, only one differential equation can be entered at one time
Repeat the similar exercise to enter the equations for 2
nd
differential equation
After pressing Done, your main window will look like this
In the window above, there is a variable that has not been specified, as indicated by the red X. The
information following the X will tell you what variables have not been specified. Here, it shows
that k1 is an undefined variable.
Now, to specify the value of k 1 , press " x= +
" button (shown by red circle in below screen). Pressing
this button brings up a different dialogue box in which you can specify explicit equations in your
system.
In this case, we only have one variable i.e.
Enter the value of ๐1 in the space provided in the rectangular box as shown below
Now, enter the final value of t i.e. t=
Press OK. When all of the necessary information has been specified, the screen will look like this.
You can check that X is now replaced by โReady for solutionโ
You can choose the method of ODE solver you would like to use by selecting the option from the
drop down menu present next to RKF45. By default, polymath uses RKF45 method. In this case,
we will choose RKF
Now select what you want polymath to output by checking the boxes on the right side of the
window. The simulation will output results depending on what is selected. The options available
are Table, Graph, and Report. Select the appropriate option and then Click on the pink
arrow to have Polymath perform the integration.
If you selected "Report" then following screen will be displayed.
Selecting "Table" will cause a data table to be generated. It includes the values of the variables at
each different step in the differential variable, in this case, time t.
To get an output that you had not previously selected, you will need to check the corresponding box
and rerun the simulation by clicking on the pink arrow.
