S3_NumericalAlgorithm

This repository regroup all the algorithm, I wrote them during my third semester at EPL in Numerical Algorithm subject. I gather them in this repository. These algorithms are writting especially in python

TABLE OF CONTENTS

• Resolution of type equation f(x) = 0
• Resolution of type equation AX = B
• Differential equation
• Interpolation

First of all, we will focusing on the first major part the subject.

Resolution of type equation f(x) = 0

We have many methods of solving but here, we will deal with four or even five methods of resolution :

• Dichotomy (Bisection) method
• Corde method
• Newton Raphson method
• Substitution (Fixed point) method

Dichotomy (Bisection) method

• The input :

 - the function to verify
 - the limits of the interval [a, b]
 - the precision p (tolerance)

• The output :

 - the solution interval [a, b]
 - the x tilde value
 - number of iterations

Corde method

• the input :

 - the function to verify
 - limits of the interval
 - the precision p (tolerance)
 - number of iterations

• the output :

 - verification of the convergence
 - the solution interval
 - the x tilde value
 - the number of iterations

Newton Raphson method

• the input :

 - the function to verify
 - the derivative the the function to verify
 - the limits of the interval
 - the maximum number of iterations

• the output :

 - the solution interval
 - the x tilde value
 - the number of iterations

Substitution (Fixed point) method

• the input :

 - the function to verify
 - the limits of the interval
 - the precision p (tolerance)
 - the maximum number of iterations

• the output :

 - the solution interval
 - the x tilde value
 - the number of iterations

Resolution of type equation AX = B

Differential equation

Interpolation