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

[Display omitted] ► 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. The network metho...

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Bibliographic Details
Published in:Computers & electrical engineering 2012-11, Vol.38 (6), p.1524-1533
Main Authors: Alhama, I., Alhama, F., Soto Meca, A.
Format: Article
Language:English
Subjects:
Computer simulation
Derivatives
Differential equations
Mathematical analysis
Mathematical models
Networks
Nonlinearity
Oscillators
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Summary:[Display omitted] ► 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. 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.
ISSN:0045-7906
1879-0755
DOI:10.1016/j.compeleceng.2012.05.008