Boundary Value Problems

Abstract

Consider a simple circuit loop with an inductor of 1 H, a resistor of 10 Ω and a capacitor of 0.25 F, as shown in Fig. 13.1. This circuit can be modelled by the following ODE:

$$ {I}^{(2)}(t)+10{I}^{(1)}(t)+4I(t)= \cos (t) $$

This model would be easy to use if the initial value of the current and its derivative was known. But what if the rate of change of the current is not known, and the only information available is the current in the circuit the moment the system was turned on and when it was shut down? That is to say, only the initial and final values of the current are known, while its derivatives are unknown.