How to define piecewise function of multiple variables?

I need to create a piecewise function in Matlab where I have a differential equation I'm trying to use ode45 on where dfdt=@(t,x) (A/B)*E + (E/A) - (A/C)*x - x*B; A,B, and C are all known constants. The function inputs for dfdt are t and x, and I need the t there too because I'm going to use ode45. Here's where it gets weird, E is a constant too but it's value changes depending on what t is. If 35<t<246 then E is 7. Otherwise, E is 1. Any help?

Answer 1

[Walter Roberson]

You cannot use piecewise functions with any of the ode* routines. The ode* routines expect that the function is continuous and will complain if the derivative of any of the computed values has a singularity.

You need to run ode45 multiple times, once for each time span that has a continuous E. Take last time's output values as the input values for the next ode call.

[Hunter Weaver]

Thanks for your help, but what do you mean by taking last time's output values as the input values for the next ode call? In my case, I would run ode45 3 times right?

[Walter Roberson]

 E = [1, 7, 1];
  x0 = ...
 [t1, x1] = ode45(@(t,x) @(t,x) (A/B)*E(1) + (E/A) - (A/C)*x - x*B, [0 35], x0);
 [t2, x2] = ode45(@(t,x) @(t,x) (A/B)*E(2) + (E/A) - (A/C)*x - x*B, 35 246], x1(end,:));
 [t3, x3] = ode45(@(t,x) @(t,x) (A/B)*E(3) + (E/A) - (A/C)*x - x*B, [246 ENDPOINT], x3(end,:));

t = [t1; t2(2:end); t3(2:end)];
x = [x1; x2(2:end,:); x3(2:end,:)];

The 2:end in calculating the final variable is to avoid having two copies of the output at the boundary times.