I need to solve numerically an equation of the form
v(t) = k1*z(t)*w(t)-k2*i(t)-k3*di(t)/dt
The issue is that rungekutta methods are useful for solving
di(t)/dt = 1/k3 * [ k1*z(t)*w(t)-k2*i(t)-k3*-v(t) ]
but I need to solve for v(t)
What I did was:
v (t) = k1*z(t)*w(t)-k2*i(t)-k3*[i(t)-i(t-1)]/h
But is not a good approximation because the step size h cannot be small enough. I need a more sophisticated method than directly applying the difference quotient as I did.
Thanks a lot!