Path following circuits - SPICE-oriented numerical methods where formulas are described by circuits $

In this paper, it is shown that various scientific problems such as fixed-point problems, linear programming problems, and nonlinear programming problems can be solved by using the circuit simulator SPICE. The basic idea of the proposed method is that formulas of the homotopy method are described by circuits, and then they are solved by SPICE. Since SPICE is an excellent software that includes various excellent techniques, this approach will make the numerical analysis very efficient, especially for stiff problems. Moreover, for SPICE users, the proposed method will be useful because they can easily solve a broad class of problems by the homotopy method realized on SPICE without programming, although they do not know the homotopy method well.