A numerical technique for computing switching transients in multiphase nonlinear systems is presented. The nonlinear terminal characteristics of the lumped parameters have been considered in totality without approximating them as piecewise linear characteristics It has been shown that a fast, stable and accurate algorithm results from using Bergeron's method of characteristics for distributed parameter lines and a semi-implicit Runge—Kutta method for solution of the differential equations which describe the dynamics of linear/nonlinear lumped parameters.