Multistep and one-leg methods for implicit mixed differential algebraic systems

General one-leg and multistep methods for mixed systems of implicit differential equations and algebraic constraints are defined. Such systems are encountered frequently in circuit analysis. Three different implementations of an -contractive two-step Adams method are shown to be second-order accurate by an analysis of the local truncation errors. These methods are tested numerically against the familiar two-step second-order backward differentiation method.