Solutions of Circuits with Fractional, Nonlinear Elements by Means of a SubIval Solver

  • Marcin SowaEmail author
Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 496)


The work concerns the application of a solver based on SubIval (the subinterval-based method for computations of the fractional derivative in initial value problems). A general form of a system of equations is considered. The system is one that can be formulated for a circuit with fractional elements, nonlinear elements and elements that are both fractional and nonlinear. A few details are given on the computations that need to be performed in each time step. An example with fractional, nonlinear elements is introduced to display the usefulness of the solver. The results obtained through the solver are compared with ones obtained through a harmonic balance methodology (steady state solution). Finally, a measure of the accuracy of the results is introduced and computed for the selected example.


Fractional derivative Numerical method Nonlinear Circuit analysis Integrodifferential equations SubIval 


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© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Silesian University of TechnologyGliwicePoland

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