AbstractThis paper describes a method of determining the forced periodic steady state response of non‐linear circuits. the method is closely related to the work of Aprille and TrickProc. IEEE,60, 108‐114 (1972) and also to the finite difference method for solving a boundary value problem.The new approach is a shooting method in the sense that in every iteration an initial value problem is solved. It is, however, also a relaxation method, because in every iteration a periodic wave‐form is obtained. This is achieved by solving in each step a linear time‐dependent differential equation whose solution can be easily transformed into a periodic solution satisfying this linear equation. Because the iteration takes place on wave‐forms rather than initial values and every solution satisfies the boundary conditions, the method is robust. It will be shown that for a causal approximation of the time derivatives the iterated wave‐forms are equal to those found using the finite differe