Process Control: Modeling, Design, and Simulation

M3.1. MATLAB ode—Basic

MATLAB has several different routines for numerical integration; all use the same basic call statements:

[t,x]= ode45('xprime',tspan,x0)   % nonstiff, medium order
[t,x]= ode23('xprime',tspan,x0)   % nonstiff, low order
[t,x]= ode113('xprime',tspan,x0)  % nonstiff, variable order
[t,x]= ode15s('xprime',tspan,x0)  % stiff, variable order
[t,x]= ode23s('xprime',tspan,x0)  % stiff, low order
[t,x]= ode23t('xprime',tspan,x0)  % moderately stiff, trapezoidal
[t,x]= ode23tb('xprime',tspan,x0) % stiff, low order

ode45 uses fourth-order and ode23 uses second-order Runge-Kutta integration. All routines use a variable integration step size (Δt is not constant). The integration step size is adjusted by the routine to provide the necessary ...