Methods

Implementation of a few numerical methods for the Computational Numerical Methods 
discipline from CIn-UFPE

Installing dependencies

1. Open the terminal and navigate to the root of the project (i.e. methods)
2. Execute: 
    sudo make
* This will make sure all the libraries are installed as well as the package 
  python-tk. 
  
* If you don't have 'make' install with: sudo apt-get install make

Running a method

1. Run: python2 start.py
* Suggestion:
    To save time you can make the input once and copy and paste it for each of the
    SINGLE step methods. For example:
        1 - t + 4*y
        0
        1
        .05
        40
    If you copy and paste these four lines when selecting any single step method
    the function 1 - t + 4*y, with (t0,y0) = (0, 1), h = .1 and number of steps 10
    will be appoximated.

    For the multi step methods, all the initial points must be given. For example:
        1 - t + 4*y
        0
        1
        .1
        1.6089333
        .2
        2.5050062
        .3
        3.8294145
        .1
        10
    This is a valid input for Adams Bashforth of fourth order, if you notice there
    are 4 points: (0,1); (.1, 1.6..); (.2, 2.5..); (.3, 3.82..)
    That is necessary because it's fourth order.

    For Adams Moulton if the order is n > 1 then you only need n-1 points ( if the
    order is n = 1, then you need one point)

2. After the method is selected the calculations will be made and a plot of the
   data will be shown. Also, the points will be displayed in the terminal while
   the plot is opened 

PS: The seventh option uses the results from the runge kutta methods as the input for the Adams multistep
methods. Careful with this one, the Inverse Euler method tends to explode in value and makes it difficult
to see the other plots. Please check the scale of the y(t) axis.

Final (AND MOST IMPORTANT) Step

1. Test all the methods and give me 100% in the project.
2. Be happy :)