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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)