# 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:

More advanced algorithms for numerical integration:

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:

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

• 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: