Numerical solver for fractional nonlinear circuit problems

Abstract

A numerical solver (applicable in GNU Octave and in Matlab) has been presented. The solver has been built in order to solve transient problems of circuit theory that feature fractional and nonlinear circuit elements (i.e. fractional coils and fractional capacitors that can even be nonlinear elements). The problems lead to a general form of fractional differential-algebraic equations. The introduced numerical solver relies on the SubIval numerical method, which is briefly recalled. The options for the solver are given and a simple circuit example containing fractional and nonlinear elements is considered. The problem is solved and the results are presented and analyzed along with the error estimation results.