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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!

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