Equivalent property between network analysis using virtual capacitors and steepest descent method

Global and stable numerical analysis algorithms of nonlinear network equations, which contain functions that are not monotonically increasing or whose differential coefficients vary broadly, include the homotopic method studied in nonlinear programming and the methods based on the insertion technique of virtual capacitors developed in Circuitsimulation. This paper shows first that these methods are almost essentially equivalent, and that the standard steepest descent method is equivalent to analyze state equations constructed by the insertion of virtual capacitors by implicit numerical integration. Moreover, a backward SD method is proposed based on the implicit use of the steepest descent method. Thic method is applied to linear and nonlinear systems, and its equivalency with the algorithms in the Circuitsimulators SRP and ASTAP using the concept of virtual capacitors is investigated. Finally, this method is applied to dc analysis, etc., of nonlinear resistive networks, and its effectiveness is verified by comparison with the results of analysis by the ASTAP method.