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The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods ab 26.49 € als Taschenbuch: Auflage 1989. Aus dem Bereich: Bücher, Wissenschaft, Mathematik,

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The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods ab 26.49 EURO Auflage 1989

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A concise introduction to numerical methodsand the mathematicalframework neededto understand their performance Numerical Solution of Ordinary Differential Equationspresents a complete and easy-to-follow introduction to classicaltopics in the numerical solution of ordinary differentialequations. The book's approach not only explains the presentedmathematics, but also helps readers understand how these numericalmethods are used to solve real-world problems. Unifying perspectives are provided throughout the text, bringingtogether and categorizing different types of problems in order tohelp readers comprehend the applications of ordinary differentialequations. In addition, the authors' collective academic experienceensures a coherent and accessible discussion of key topics,including: * Euler's method * Taylor and Runge-Kutta methods * General error analysis for multi-step methods * Stiff differential equations * Differential algebraic equations * Two-point boundary value problems * Volterra integral equations Each chapter features problem sets that enable readers to testand build their knowledge of the presented methods, and a relatedWeb site features MATLAB® programs that facilitate theexploration of numerical methods in greater depth. Detailedreferences outline additional literature on both analytical andnumerical aspects of ordinary differential equations for furtherexploration of individual topics. Numerical Solution of Ordinary Differential Equations isan excellent textbook for courses on the numerical solution ofdifferential equations at the upper-undergraduate and beginninggraduate levels. It also serves as a valuable reference forresearchers in the fields of mathematics and engineering.

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A concise introduction to numerical methodsand the mathematical framework neededto understand their performance Numerical Solution of Ordinary Differential Equations presents a complete and easy-to-follow introduction to classical topics in the numerical solution of ordinary differential equations. The book's approach not only explains the presented mathematics, but also helps readers understand how these numerical methods are used to solve real-world problems. Unifying perspectives are provided throughout the text, bringing together and categorizing different types of problems in order to help readers comprehend the applications of ordinary differential equations. In addition, the authors' collective academic experience ensures a coherent and accessible discussion of key topics, including: * Euler's method * Taylor and Runge-Kutta methods * General error analysis for multi-step methods * Stiff differential equations * Differential algebraic equations * Two-point boundary value problems * Volterra integral equations Each chapter features problem sets that enable readers to test and build their knowledge of the presented methods, and a related Web site features MATLAB(r) programs that facilitate the exploration of numerical methods in greater depth. Detailed references outline additional literature on both analytical and numerical aspects of ordinary differential equations for further exploration of individual topics. Numerical Solution of Ordinary Differential Equations is an excellent textbook for courses on the numerical solution of differential equations at the upper-undergraduate and beginning graduate levels. It also serves as a valuable reference for researchers in the fields of mathematics and engineering.

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A global zero residual least squares method.- Efficient primal algorithms for strictly convex quadratic programs.- Location of multiple equilibrium configurations near limit points by a double dogleg strategy and tunnelling.- Considerations of numerical analysis in a sequential quadratic programming method.- Remarks on a continuous finite element scheme for hyperbolic equations.- An efficient modular algorithm for coupled nonlinear systems.- Optimization of multistage processes described by differential-algebraic equations.- Polynomial iteration for nonsymmetric indefinite linear systems.- Viewing the conjugate gradient method as a trust region algorithm.- An efficient strategy for utilizing a merit function in nonlinear programming algorithms.- Rates of convergence for secant methods on nonlinear problems in hilbert space.- The construction of preconditioners for elliptic problems by substructuring.- Some superconvergence results for mixed finite element methods for linear parabolic problems.- Nodal methods for the numerical solution of partial differential equations.- Singular perturbation problems in semiconductor devices.- Stability of capillary waves on deep water.- A block 5(4) explicit runge-kutta formula with 'free' interpolation.- Sequential step control for integration of two-point boundary value problems.

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'Whatever regrets may be, we have done our best.' (Sir Ernest Shack 0 leton, turning back on 9 January 1909 at 88 23' South.) Brahms struggled for 20 years to write his first symphony. Compared to this, the 10 years we have been working on these two volumes may even appear short. This second volume treats stiff differential equations and differential algebraic equations. It contains three chapters: Chapter IV on one-step (Runge-Kutta) meth ods for stiff problems, Chapter V on multistep methods for stiff problems, and Chapter VI on singular perturbation and differential-algebraic equations. Each chapter is divided into sections. Usually the first sections of a chapter are of an introductory nature, explain numerical phenomena and exhibit numerical results. Investigations of a more theoretical nature are presented in the later sections of each chapter. As in Volume I, the formulas, theorems, tables and figures are numbered con secutively in each section and indicate, in addition, the section number. In cross references to other chapters the (latin) chapter number is put first. References to the bibliography are again by 'author' plus 'year' in parentheses. The bibliography again contains only those papers which are discussed in the text and is in no way meant to be complete.

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