Numerical analysis: solutions of ordinary differential equations with Matlab. This project was developed during a university course (Numerical methods) in 2015-2016. Comments are in Spanish, except in mispracticas.m, where the comments are in English.
##Functions
funccorazon.m - Cardioid
funcvanderpol.m - Van der Pol oscillator
funcpendulo.m - Pendulum
funcpendulolin.m - Lineal pendulum
##Auxiliar modules
mispracticas.m - in every line has an equation and its input values
misgraficas.m - to paint the solution
##Initial value problems
###One-step methods
mieuler.m - Euler method
mirk4.m - fourth-order Runge-Kutta
mitrap.m - Trapezoidal method
jacrigida - Jacobian matrix of the equation x'(t) = -50(x(t)-cos(t)) to be used in mitrap.m
jacvanderpol - Jacobian matrix of the Van der Pol oscillator equation to be used in mitrap.m
###Multistep methods
miab4.m - 4-step Adams-Bashforth method
mimilne.m - 4-step Milne method
###Predictor–corrector methods
mieulertr.m - Predictor: Euler method, Corrector: Trapezium method
miab4am3.m - Predictor: 4-step Adams-Bashforth method, Corrector: 3-step Adams-Moulton method
mimilsimp.m - Predictor: 4-step Milne method, Corrector: 2-step Simpson method
###Adaptive algorithms
mimetadap.m - Using a one-step method
mirkf45.m - Runge-Kutta-Fehlberg method
##Boundary value problems
###Linear boundary value problem
midisplin.m - linear boundary value problems for several types of boundary conditions
fundisplin1.m - ordinary differential equation used in midisplin.m
fundisplin2.m - ordinary differential equation used in midisplin.m
###Nonlinear boundary value problem
midispnolin.m - nonlinear boundary value problems for several types of boundary conditions: Dirichlet and Neumann
midispnolingen.m - generalization of midispnolin.m which can be use for more types of boundary conditions: Robin
funcdispnolin.m - used in midispnolin.m and midispnolingen.m
##Tests
All of them use the input values and function from mispracticas.m, use a method to solve the problem and misgraficas.m to paint the solution
testmiode45.m - Use Matlab function ode45
testmieuler.m - Use mieuler.m
testmirk4.m - Use mirk4.m
testmitrap.m - Use mitrap.m
testmiab4.m - Use miab4.m
testmimilne.m - Use mimilne.m
testmieulertr.m - Use mieulertr.m
testmiab4am3.m - Use miab4am3.m
testmimilsimp.m - Use mimilsimp.m
testmimetadap.m - Use mimetadap.m
testmirkf45.m - Use mirkf45.m
testmidisplin.m - Use midisplin.m
testmidispnolin.m - Use midispnolin.m
This project was developed by Ana María Martínez Gómez.
Code published under MIT License (see LICENSE).