PCSC - Project 5: Non-linear systems

Authors: Cyril Vallez, Eliott Zemour.
GROUP 7.
Implementation of numerical methods for the solution of nonlinear equations (NLE).

The numerical methods implemented are:

• Bisection,
• Fixed point methods:
  • Chord,
  • Newton

And an acceleration feature through Aitken's delta squared process is also implemented according to this source.
The main source for this project can be found at https://onlinelibrary.wiley.com/doi/pdf/10.1002/9781118673515.app8.

Finally, this project includes an extension to systems of nonlinear equations (NLS) solved by the Newton method in n-dimensions.

Requirements

This project relies on the following librairies:

• GoogleTest
• cmath
• chrono
• string
• iostream
• cstdlib

Architecture of the project

A Doxygen generated documentation is also available within the 'html' folder of the repository.

How to use

There are several ways to use the numerical methods implemented:

• Either though out of class methods Solve_Newton, Solve_Chord, Solve_Bisection are designed to instantiate the NLE Solver objects, call their own solve function to obtain the solution and then delete them. Code example:

    double function(double x)
    {
    // definition of function
    }
    
    double (*func)(double x) = &function;
    double LeftEdge = -5.;
    double RightEdge = 5.;
    double solution = Solve_Bisection(func, LeftEdge, RightEdge);

• Either by dynamically allocating memory for a NLE Solver object and directly calling its solve function. In this case the user is responsible of deleting the object. Code example:

    double function(double x)
    {
    // definition of function
    }
    
    double (*func)(double x) = &function;
    double LeftEdge = -5.;
    double RightEdge = 5.;
    NLE_Solver* solver = new Bisection_Solver(func, LeftEdge, RightEdge);
    double solution = solver->Solve();
    delete solver;