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euler's method:
dx/dt =~ ( x(t + Dt) - x(t) ) / Dt, for very small Dt
so, x(t + Dt) = x(t) + f(x) * Dt, which is how to integrate the system
"if Dt is too large, becomes highly unstable" (duh)
scary MATLAB advice:
- watch out of totally crazy values (very high)
- non-negative values go negative
MATLAB built-in ODE solvers: ode23, ode15s
runge-kutta (use dxdt from between t_n and t_(n+1) )
variable time-step methods
summary: Euler's method sucks, news at 11.
### misc julia notes
the only place to find history (?!?!!) is in ~/.julia_history
### codes
using Winston
a=20
b=2
c=5
dt = 0.05
tlast = 2
iterations = int( round(tlast/dt) )
xall = zeros(iterations, 1)
x = c
for i = 1:iterations
xall[i] = x
dxdt = a - b*x
x = x + dxdt*dt
end
time = dt * [0:iterations-1]'
plot(time,xall)
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