CauchyProblem

This package implements different numerical methods for solving Cauchy problem.

Application

This package also solves task that involves differential equations by using those numerical methods. The task is in the 'executable/task.png' file.

Solution uses four differential equations: two for second derivative (acceleration) that are already given and that the first derivative is the speed. We have initial values for all four equations (dx/dt, dv_x/dt, dy/dt, dv_y/dt), so the task now becomes just a Cauchy Initial Value Problem!

In the 'executable' folder you can find executable for solving, testing and many more! It has two command line arguments -

1. ./CauchyProblem X11 uses Linux X11 to interactively display plot of solution (works only if X11 is installed on your system).
2. ./CauchyProblem PNG filename saves plot to file (due to absence of interactivity you may not like chosen scaling - but usually it is fine if you tweak initial values).

By default it saves plot to 'plots/plot.png' file.

There are few configurations in the executable itself - it will ask some input from you, so just follow instuctions that are given to you by the app.

Some examples (you can find them at 'executable/examples'):

1. v0_x = 0, v0_y = 0 gives us simple circular orbit

2. v0_x = 2.5, v0_y = 1 gives us elliptical orbit

3. v0_x = -5, v0_y = 0 crashes our satellite

4. t1 = 20000, v0_x = -3, v0_y = 5 sends our satellite on hyperbolic orbit (note how fast that is that you even have to change time to see it better on the plot!)

Dependencies

This package is built in Haskell by using only one library - easyplot, which is source of external dependency, since it uses gnuplot to provide plotting API.

gnuplot is the only required dependency, but if you want to play with source code and compile the solution, you will need to install Haskell and install easyplot via cabal. You will be able to find nice guidelines on how to do that in the Internet.