stepwise ode. why does this fail?

*To*: mathgroup at smc.vnet.net*Subject*: [mg48415] stepwise ode. why does this fail?*From*: sean_incali at yahoo.com (sean kim)*Date*: Fri, 28 May 2004 00:51:04 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

Why does this fail? I don't understand. I think it's because the function defining the a0 is delayed... is that right? if so, how do i define a stepwise ode in Mathematica? I wanted to make a0= 0 at time 0, then 1/20 for given time then 0 and again opver next time frame then 1/20 again for the rest of the time. below is my attempt. but it brings back NDSolve::ndnum: Encountered non-numerical value for a derivative at t == 0. k1 = 1/10; k2 = 1/20; a0 := 0 /; t < 0 ; a0 := 1/20 /; 0 <= t <= 200 ; a0 := 0 /; 200 <= t <= 600 ; a0 := 1/20 /; 600 <= t <= 1000; ndsolution = NDSolve[{b'[t] == -k2 b[t] y[t], x'[t] == -k1 a0 x[t] + k2 b[t] y[t], y'[t] == k1 a0 x[t] - k2 b[t] y[t], b[0] == 1, x[0] == 1, y[0] == 0}, {b, x, y}, {t, 0, 1000}] thanks all very much in advance for any and all comments. sean