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Piecewise-linear (PWL) functions are frequently used to describe the nonlinear branch equations of nonlinear devices in LSI circuits. New techniques for the solution of the differential equations describing the behavior of piecewise-linear circuits will be presented. These techniques are based on the waveform relaxation method to decouple the system equations and Laplace transform techniques to solve the decoupled equations. Several desirable features of the resulting algorithm are discussed.