Implicit System Of Differential Equations Research Articles

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 <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A (\alpha)</tex> -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.

Quadratures for Implicit Differential Equations

Quadrature methods are used to obtain numerical solutions of certain systems of implicit differential equations. Development of the methods leads to an extension of an existence theorem for implicit differential equations. Several examples indicate the range of application of the methods.