Math 579 > Matlab files

Matlab files

Here you can find some m-files with commentaries. To see the commentary, type

>> help filename

in Matlab command window. (here 'filename' should be replaced by actual name, for instance, euler).

Disclaimer: These files are provided "as is", without warranties of any kind.

Some fixed-stepsize Runge-Kutta type solvers for initial value problems:
  • Euler's method for scalar equations: euler1.m
  • Heun's method for scalar equations: heun1.m
  • The midpoint method for scalar equations: midpoint1.m
  • (General) Euler's method: euler.m
  • (General) Heun's method: heun.m
  • The (general) midpoint method: midpoint.m
  • Runge-Kutta method of order 4: rk4.m
One step at a time: Stability region: Some examples of modeling and simulation by IVPs: Variable step-size (aka adaptive) methods:
  • Runge-Kutta-Fehlberg order 4/order 5 embedded pair: rkf45.m
Implicit methods:
  • Backward Euler with Newton's method as a solver (fixed step-size): beuler.m
Equation solvers:
  • A simple implementation of Newton's method: newton.m
  • A simple implementation of the secant method: secant.m
Multistep methods:
  • Adams-Bashforth 4-step method: ab4.m
  • Adams-Bashforth / Adams-Moulton predictor-corrector pair of order 4: abm4.m
Shooting methods for 2nd order (Dirichlet) boundary value problems:
  • Linear shooting method (with fixed stepsize IVP solvers): linshoot.m
  • Shooting method using bisection (with fixed stepsize IVP solvers): bisectshoot.m
  • Shooting method using bisection (with Runge-Kutta-Fehlberg 4/5 variable stepsize solver): rkf45bisectshoot.m
Finite difference methods for 2nd order (Dirichlet) boundary value problems:
  • For linear problems: linfd.m
  • For nonlinear problems (using a fixed point iteration): fpifd.m
  • For nonlinear problems (using Newton's iteration): newtfd.m

MATH 579: Numerical Differential Equations Winter 2010