Numerical Methods

Before executing the code:

It is necessary to have python installed, and also PIP. On the terminal of commands, type:

python -m pip install sympy

The command above installs "sympy" library for Python, as this code uses it for derivative and trigonometric calcuations.

For executing the program:

You need to type the fields below to execute the program on terminal (on the same directory the code is in):

python methods.py <method> <f> <a/x0> <b/x1> <eps> <fi(opt)>

Available methods: bis, pf, mil, nr, sec. Relation of methods:

• bis: Bissection Method;
• pf: False Position Method (Regula Falsi);
• mil: Fixed Point Iteration Method;
• nr: Newton_Rhapson Method;
• sec: Secant Method;

Obs.:

• The last "fi" parameter will only be used for the Fixed Point Iteration Method;
• On the secant method, a and b are x_k-1 and x_k, respectively;

Use cases:

Example of every described method solving x³-9x+3=0, ε=10⁻²:

python methods.py mil x**3-9*x+3 0 1 0.01 '(x**3+3)/9'
python methods.py sec x**3-9*x+3 0 1 0.01
python methods.py bis x**3-9*x+3 0 1 0.01
python methods.py pf x**3-9*x+3 0 1 0.01
python methods.py nr x**3-9*x+3 0 1 0.01

PS.: When using parenthesis be sure to use single quotes around the whole formula. Exponentiation in Python is made by using double * (Ex.: a² equal to a**2).