The network method for a fast and reliable solution of ordinary differential equations: Applications to non-linear oscillators

The network method is used for designing electric circuits that implement any kind of linear and non-linear ordinary differential equations of any grade and any order. The model simulations are carried out in a suitable computational code without any other mathematical manipulation. The addends of the equation are assumed to be electric currents that balance each other in the only common node of the main loop. Four special kinds of controlled source, named voltage-controlled (or current-controlled) voltage-source and voltage-controlled (or current-controlled) current-source, in conjunction with auxiliary simple circuits are used to implement derivative terms other kinds of non-linear character terms. Applications are shown which demonstrate the reliability and power of the proposed method.

Graphical abstractFigure optionsDownload full-size imageDownload as PowerPoint slideHighlights► Simulation of non-linear ordinary differential equations, of any grade and any order, by network method (electrical analogy). ► The rules for the design the models are few and intuitive. ► Non-linear equations that represent chaotic systems are easily simulated.