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
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