Matlab files

Here you can find some m-files that are not posted in 'Lectures' part, as well as the existing 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, midp).

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

Here is a user-defined function, which can be modified and used as an input to the numerical integration or differentiation subroutines below: myfunc.m

Finite difference formulas for numerical differentiation:

• Two-point forward difference formula for first derivative: d1fd2p.m
• Three-point centered-difference formula for first derivative: d1cd3p.m
• Three-point centered-difference formula for second derivative: d2cd3p.m
• Two-point forward difference formula for first derivative, varying h: d1fd2p_varh
• Three-point centered-difference formula for first derivative, varying h: d1cd3p_varh.m
• Three-point centered-difference formula for second derivative, varying h: d2cd3p_varh.m

Composite Newton-Cotes rules for numerical integration:

• Trapezoid rule: trap.m
• Simpson's rule: simp.m
• Newton's rule: newt.m
• Boole's rule: boole.m
• Midpoint rule: midp.m
• Two-point open rule: mid2p.m
• Three-point open rule: mid3p.m

More advanced algorithms for numerical integration:

• Romberg integration: romberg.m
• Adaptive trapezoid method (uses trap.m above): adaptrap.m

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:

• One step of Euler's method: eulerstep.m
• One step of Heun's method: heunstep.m
• One step of the midpoint method: midpointstep.m
• One step of Runge-Kutta method of order 4: rk4step.m
• A fixed-stepsize solver that can use any of the above as steps: solver1.m

Some examples of modeling and simulation by IVPs:

• Pendulum (the bug is fixed by Matt Comber): pend.m
• Two-body problem (modification of the program for one-body problem): orbit2.m

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