ORDINARY DIFFERENTIAL EQUATIONS AND TIME-STEPPING: Using the definition of derivative and Taylor series, numerical time-stepping schemes are produced for predicting the future state of ODE systems.

MATLAB COMMANDS

`n/a`

MATLAB CODE

ERROR AND STABILITY OF TIME-STEPPING SCHEMES: The accuracy and stability of time-stepping schemes are considered and compared on various time-stepping algorithms.

MATLAB COMMANDS

`n/a`

GENERAL TIME-STEPPING AND RUNGE-KUTTA SCHEMES: A general framework for time-stepping schemes is developed, culminating in the 4th-order accurate Runge-Kutta scheme which is the work-horse of many applications.

MATLAB COMMANDS

`ODE45`