The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods / Edition 1

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Overview

The term differential-algebraic equation was coined to comprise differential equations with constraints (differential equations on manifolds) and singular implicit differential equations. Such problems arise in a variety of applications, e.g. constrained mechanical systems, fluid dynamics, chemical reaction kinetics, simulation of electrical networks, and control engineering. From a more theoretical viewpoint, the study of differential-algebraic problems gives insight into the behaviour of numerical methods for stiff ordinary differential equations. These lecture notes provide a self-contained and comprehensive treatment of the numerical solution of differential-algebraic systems using Runge-Kutta methods, and also extrapolation methods. Readers are expected to have a background in the numerical treatment of ordinary differential equations. The subject is treated in its various aspects ranging from the theory through the analysis to implementation and applications.

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Product Details

  • ISBN-13: 9783540518600
  • Publisher: Springer Berlin Heidelberg
  • Publication date: 12/11/1989
  • Series: Lecture Notes in Mathematics Series , #1409
  • Edition description: 1989
  • Edition number: 1
  • Pages: 146
  • Product dimensions: 9.21 (w) x 6.14 (h) x 0.33 (d)

Table of Contents

Description of differential-algebraic problems.- Runge-Kutta methods for differential-algebraic equations.- Convergence for index 1 problems.- Convergence for index 2 problems.- Order conditions of Runge-Kutta methods for index 2 systems.- Convergence for index 3 problems.- Solution of nonlinear systems by simplified Newton.- Local error estimation.- Examples of differential-algebraic systems and their solution.

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