The application of numerical methods based on polynomial approximation and multistep algorithms is presented to simulate the behavior of a chaotic oscillator, e.g. Chua’s circuit, which consist of five circuit elements: one linear resistor, one inductor, two capacitors and one nonlinear resistor known as Chua’s diode. The last element is modeled by an I-V piecewise-linear function to formulate a system of linear dynamic equations. This initial value problem is solved by applying numerical simulation to compute a sequence of chaotic phenomena by solving the state-variables equations describing Chua’s circuit. It is highlighted the usefulness of numerical methods to speed-up time simulation to estimate the values of the circuit elements, so that the synthesis of Chua’s diode can be realized directly using novel active devices. For instance, it is described the synthesis of Chua’s circuit using SPICE and standard CMOS integrated-circuit technology of 0.35μm, to show the control of the I-V slopes and the generation of chaotic phenomena which are in good agreement with that computed from numerical simulation.