Some problems in the T-analysis of nonlinear electric networks

The paper examines methods for the optimal approximation of nonlinear characteristics (prescribed in an analytical or tabular way) by lower-order spline functions involving the use of best-approximation polynomials. An algorithm based on differential transforms is developed for obtaining several solutions for resistive nonlinear networks. The algorithm uses homotopy connecting the initial system of nonlinear algebraic equations with a certain elementary system of equations with unknown solutions. An implicit T-scheme of numerical integration is described which is applicable to the analysis of linear networks with piecewise-linear characteristics.