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Umfang: 1 online resource (317 p.)

ISBN: 1-282-61872-5 , 9786612618727 , 0-08-095583-5

Serie: Mathematics in science and engineering ; v. 74

Inhalt: In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank

Anmerkung: Description based upon print version of record. , Front Cover; Numerical Solution of Ordinary Differential Equations; Copyright Page; Contents; Preface; Chapter 1. Fundamental Definitions and Equations; 1.1 The Numerical Problem and Nomenclature; 1.2 Taylor Series Expansion; 1.3 Aspects of Numerical Interpolation; 1.4 Differentiation Formulas; 1.5 Specific Integration Formulas; 1.6 Integration Formulas for ODE; 1.7 Generalized Integration Formulas for ODE; 1.8 Compilation of Various Multiple-Step Integration Formulas Including yi and yi`; 1.9 Compilation of Various Multiple-Step Formulas Including y, and yi`` , 1.10 Multiple-Step Integration Formulas: Higher Derivative Terms1.11 Further Definitions; References; Chapter 2. Runge-Kutta and Allied Single-Step Methods; 2.1 Development of Single-Step Runge-Kutta Formulas; 2.2 Condensed Nomenclature for Runge-Kutta Methods; 2.3 Explicit Runge-Kutta Equations of Different Order; 2.4 Runge-Kutta Formulas Derived from Truncation Error Analysis; 2.5 Quadrature and Implicit Formulas; 2.6 Runge-Kutta Formulas for Vector Differential Equations; 2.7 Two-Step Runge-Kutta Formulas; 2.8 Local Truncation Error Estimates in a Single Step , 2.9 Local Truncation Error Estimate in Two Steps2.10 Local Truncation Error Estimates in More than Two Steps; 2.11 Local Round-Off Error in Single-Step Methods; 2.12 The Explicit Use of Single-Step Formulas; 2.13 Modern Taylor Series Expansions; 2.14 Published Numerical Results; 2.15 Numerical Experiments; References; Chapter 3. Stability of Multistep and Runge-Kutta Methods; 3.1 Linear Multistep Methods; 3.2 Numerical Stability of Linear Multistep Methods; 3.3 Dahlquist Stability Theorems; 3.4 Stability of Multistep Methods in Integrating Coupled ODEs , 3.5 Stability of Integration of Nonlinear ODEs3.6 Stability of Runge-Kutta Methods; 3.7 Stability of Single-Step Methods Employing Second Derivatives; 3.8 Stability versus Accuracy; 3.9 Published Numerical Results; 3.10 Numerical Experiments; References; Chapter 4. Predictor-Corrector Methods; 4.1 A Simple Predictor-Corrector Set; 4.2 A Modified Predictor-Corrector Set; 4.3 Convergence of Iterations in the Corrector; 4.4 Accuracy and Stability for Some Simple Predictor-Corrector Methods; 4.5 Milne Predictor-Corrector Forms; 4.6 Hamming Predictor-Corrector Set , 4.7 Adams Predictor-Corrector Set4.8 PE(CE)s versus P(EC)s Combinations; 4.9 Special Second-Order Differential Equations; 4.10 Use of Higher-Order Derivative P-C Combinations; 4.11 Hybrid Type Methods; 4.12 Starting the P-C Computation; 4.13 Adjustment of the Step Size during the P-C Solution; 4.14 Tabulation of Equations and Stability Bounds; 4.15 Published Numerical Results; 4.16 Numerical Experiments; 4.17 Numerical Comparisons of Single- and Multiple-Step Methods; References; Chapter 5. Extrapolation Methods; 5.1 Extrapolation to the Limit; 5.2 Extrapolation Algorithms for ODE , 5.3 Stability and Error Analysis of Extrapolation Methods , English

Weitere Ausg.: ISBN 0-12-436650-3

Sprache: Englisch

UID:

Umfang: Online Ressource (xii, 299 pages)

Ausgabe: Online-Ausg. [S.l.] HathiTrust Digital Library Online-Ausg. [S.l.] : HathiTrust Digital Library

ISBN: 0124366503 , 9780080955834 , 0080955835 , 9780124366503

Serie: Mathematics in science and engineering v. 74

Inhalt: A concise introduction to numerical methods and the mathematical framework needed to understand their performance

Anmerkung: Includes bibliographical references and index. - Print version record , Print version record , Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002 , Front Cover; Numerical Solution of Ordinary Differential Equations; Copyright Page; Contents; Preface; Chapter 1. Fundamental Definitions and Equations; 1.1 The Numerical Problem and Nomenclature; 1.2 Taylor Series Expansion; 1.3 Aspects of Numerical Interpolation; 1.4 Differentiation Formulas; 1.5 Specific Integration Formulas; 1.6 Integration Formulas for ODE; 1.7 Generalized Integration Formulas for ODE; 1.8 Compilation of Various Multiple-Step Integration Formulas Including yi and yi`; 1.9 Compilation of Various Multiple-Step Formulas Including y, and yi`` , 1.10 Multiple-Step Integration Formulas: Higher Derivative Terms1.11 Further Definitions; References; Chapter 2. Runge-Kutta and Allied Single-Step Methods; 2.1 Development of Single-Step Runge-Kutta Formulas; 2.2 Condensed Nomenclature for Runge-Kutta Methods; 2.3 Explicit Runge-Kutta Equations of Different Order; 2.4 Runge-Kutta Formulas Derived from Truncation Error Analysis; 2.5 Quadrature and Implicit Formulas; 2.6 Runge-Kutta Formulas for Vector Differential Equations; 2.7 Two-Step Runge-Kutta Formulas; 2.8 Local Truncation Error Estimates in a Single Step , 2.9 Local Truncation Error Estimate in Two Steps2.10 Local Truncation Error Estimates in More than Two Steps; 2.11 Local Round-Off Error in Single-Step Methods; 2.12 The Explicit Use of Single-Step Formulas; 2.13 Modern Taylor Series Expansions; 2.14 Published Numerical Results; 2.15 Numerical Experiments; References; Chapter 3. Stability of Multistep and Runge-Kutta Methods; 3.1 Linear Multistep Methods; 3.2 Numerical Stability of Linear Multistep Methods; 3.3 Dahlquist Stability Theorems; 3.4 Stability of Multistep Methods in Integrating Coupled ODEs , 3.5 Stability of Integration of Nonlinear ODEs3.6 Stability of Runge-Kutta Methods; 3.7 Stability of Single-Step Methods Employing Second Derivatives; 3.8 Stability versus Accuracy; 3.9 Published Numerical Results; 3.10 Numerical Experiments; References; Chapter 4. Predictor-Corrector Methods; 4.1 A Simple Predictor-Corrector Set; 4.2 A Modified Predictor-Corrector Set; 4.3 Convergence of Iterations in the Corrector; 4.4 Accuracy and Stability for Some Simple Predictor-Corrector Methods; 4.5 Milne Predictor-Corrector Forms; 4.6 Hamming Predictor-Corrector Set , 4.7 Adams Predictor-Corrector Set4.8 PE(CE)s versus P(EC)s Combinations; 4.9 Special Second-Order Differential Equations; 4.10 Use of Higher-Order Derivative P-C Combinations; 4.11 Hybrid Type Methods; 4.12 Starting the P-C Computation; 4.13 Adjustment of the Step Size during the P-C Solution; 4.14 Tabulation of Equations and Stability Bounds; 4.15 Published Numerical Results; 4.16 Numerical Experiments; 4.17 Numerical Comparisons of Single- and Multiple-Step Methods; References; Chapter 5. Extrapolation Methods; 5.1 Extrapolation to the Limit; 5.2 Extrapolation Algorithms for ODE , 5.3 Stability and Error Analysis of Extrapolation Methods , Online-Ausg. [S.l.] : HathiTrust Digital Library , Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002.

Weitere Ausg.: ISBN 0124366503

Weitere Ausg.: Erscheint auch als Druck-Ausgabe Lapidus, Leon Numerical solution of ordinary differential equations New York, Academic Press, 1971

Sprache: Englisch

Schlagwort(e): Electronic books

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