All the content, including figures, bibliography, front page, etc. of my undergraduate thesis (in Spanish). Written in Latex.
- Title: "Numerical methods for nonlinear modeling"
- Description: In this work we have tried and succeeded in designing new iterative methods for solving nonlinear equations and systems; these are compared with the already existing ones and it has been found that they are highly efficient and stable. Then, we applied these methods to some nonlinear equations which have a recognized physical interest: Bratu's problem and Burgers's equation; in both cases the goal is to find the solution of a nonlinear partial differential equation. Because the design has resulted in families of methods instead of unique methods, we used the dynamical techniques in order to choose which members of the family (although all of them have the same order of convergence) are the most stable. Furthermore, we have also designed and studied a new way of discretizing Burgers's equation in order to increase the accuracy of the solution and simplify the process of obtaining it.
The main files are titled tesis.tex and tesis.pdf