The numerical solution of differential-algebraic systems by Runge-Kutta methods / Ernst Hairer, Christian Lubich, Michel Roche

Differential-algebraic systems arise and have to be solved in a variety of applications, e.g., constrained mechanical systems, fluid dynamics, chemical reaction kinetics, simulation of electrical networks, and control engineering. Runge-Kutta methods can be applied advantageously to such systems and they distinguish themselves by interesting properties.
In the first two sections the authors describe the differential-algebraic problems and the use of Runge-Kutta methods. In Sections 3 to 6 existence and uniqueness of the numerical solution, influence of perturbations, local error and convergence, and asymptotic expansions are studied. The handling of the arising nonlinear equations by the simplified Newton method is discussed and local error estimates are investigated in Sections 7 and 8. The final sections are devoted to examples of differential-algebraic systems which are integrated with the implicit Runge-Kutta code RADAU5 developed by the authors.
In a convincing manner the authors succeed in treating the subject from theory via numerical analysis to implementation and applications. Decidedly, the monograph addresses a large circle of persons concerned. (MathSciNet)