Recently, efficient algorithms have been proposed for finding all characteristic curves of one-port piecewise-linear (PWL) resistive circuits. Using these algorithms, a middle scale one-port circuit can be represented by a PWL resistor that is neither voltage nor current controlled. By modeling often used one-port subcircuits by such resistors (macromodels), large scale circuits can be analyzed efficiently. In this paper, an efficient method is proposed for finding DC operating points of nonlinear circuits containing such neither voltage nor current controlled resistors using the SPICE-oriented approach. The proposed method can be easily implemented on SPICE without programming.

As a powerful computational test for nonexistence of a DC solution of a nonlinear circuit, the LP test is well-known. This test is useful for finding all solutions of nonlinear circuits; it is also useful for verifying the nonexistence of a DC operating point in a given region where operating points should not exist. However, the LP test has not been widely used in practical circuit simulation because the programming is not easy for non-experts or beginners. In this paper, we propose a new LP test that can be easily implemented on SPICE without programming. The proposed test is useful because we can easily check the nonexistence of a solution using SPICE only.

Recently, an efficient homotopy method termed the variable gain Newton homotopy (VGNH) method has been proposed for finding DC operating points of nonlinear circuits. This method is not only very efficient but also globally convergent for any initial point. However, the programming of sophisticated homotopy methods is often difficult for non-experts or beginners. In this paper, we propose an effective method for implementing the VGNH method on SPICE. By this method, we can implement a "sophisticated VGNH method with various efficient techniques" "easily" "without programming," "although we do not know the homotopy method well."

Path following circuits (PFC's) are circuits for solving nonlinear problems on the circuit simulator SPICE. In the method of PFC's, formulas of numerical methods are described by circuits, which are solved by SPICE. Using PFC's, numerical analysis without programming is possible, and various techniques implemented in SPICE will make the numerical analysis very efficient. In this paper, we apply the PFC's of the homotopy method to various nonlinear problems (excluding circuit analysis) where the homotopy method is proven to be globally convergent; namely, we apply the method to fixed-point problems, linear programming problems, and nonlinear programming problems. This approach may give a new possibility to the fields of applied mathematics and operations research. Moreover, this approach makes SPICE applicable to a broader class of scientific problems.