
3
Elementary Numerical
Integration
3.1 INTRODUCTION
Dynamic systems with continuous-time models in the form of differential equations possess
memory. For systems with memory, knowledge of the system’s inputs at a given point in time is
insufficient to determine the state of the system at the same time. For example, a circuit with
capacitors and inductors possesses memory. The instantaneous energy stored in the circuit is a
function of the current state (capaci tor voltages and inductor currents), whi ch depends on the history
of its sources (inputs) from the time when the complete state was last known.
An nth-order dynamic system with state variables