ana06 / ode

Numerical analysis: solutions of ordinary differential equations with Matlab

ODE

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

Authors

This project was developed by Ana María Martínez Gómez.

Licence

Code published under MIT License (see LICENSE).