Introduction to numerical methods for time dependent differential equations / / Heinz-Otto Kreiss, Omar Eduardo Ortiz

• Autore: Kreiss H (Heinz-Otto)
• Pubblicazione: Hoboken, New Jersey : , : Wiley, , 2014; ©2014
• Descrizione fisica: 1 online resource (314 p.)
• Disciplina: 515/.353
• Soggetto topico: Differential equations, Partial - Numerical solutions
• Soggetto genere / forma: Electronic books.
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Cover; Half Title page; Title page; Copyright page; Dedication; Preface; Acknowledgements; Part I: Ordinary Differential Equations and Their Approximations; Chapter 1: First-Order Scalar Equations; 1.1 Constant coefficient linear equations; 1.2 Variable coefficient linear equations; 1.3 Perturbations and the concept of stability; 1.4 Nonlinear equations: the possibility of blow-up; 1.5 Principle of linearization; Chapter 2: Method of Euler; 2.1 Explicit Euler method; 2.2 Stability of the explicit Euler method; 2.3 Accuracy and truncation error ; 2.4 Discrete Duhamel's principle and global error2.5 General one-step methods; 2.6 How to test the correctness of a program; 2.7 Extrapolation; Chapter 3: Higher-Order Methods; 3.1 Second-order Taylor method; 3.2 Improved Euler's method; 3.3 Accuracy of the solution computed; 3.4 Runge-Kutta methods; 3.5 Regions of stability; 3.6 Accuracy and truncation error; 3.7 Difference approximations for unstable problems; Chapter 4: Implicit Euler Method; 4.1 Stiff equations; 4.2 Implicit Euler method; 4.3 Simple variable-step-size strategy; Chapter 5: Two-Step and Multistep Methods ; 5.1 Multistep methods5.2 Leapfrog method; 5.3 Adams methods; 5.4 Stability of multistep methods; Chapter 6: Systems of Differential Equations; Part II: Partial Differential Equations and Their Approximations; Chapter 7: Fourier Series and Interpolation; 7.1 Fourier expansion; 7.2 L2-norm and scalar product; 7.3 Fourier interpolation; Chapter 8: 1-Periodic Solutions of time Dependent Partial Differential Equations with Constant Coefficients; 8.1 Examples of equations with simple wave solutions ; 8.2 Discussion of well posed problems for time dependent partial differential equations with constant coefficients and with 1-periodic boundary conditionsChapter 9: Approximations of 1-Periodic Solutions of Partial Differential Equations; 9.1 Approximations of space derivatives; 9.2 Differentiation of Periodic Functions; 9.3 Method of lines; 9.4 Time Discretizations and Stability Analysis; Chapter 10: Linear Initial Boundary Value Problems; 10.1 Well-Posed Initial Boundary Value Problems; 10.2 Method of lines; Chapter 11: Nonlinear Problems ; 11.1 Initial value problems for ordinary differential equations11.2 Existence theorems for nonlinear partial differential equations; 11.3 Nonlinear example: Burgers' equation; Appendix A: Auxiliary Material; A.1 Some useful Taylor series; A.2 "O" notation; A.3 Solution expansion; Appendix B: Solutions to Exercises; References; Index
• Sommario/riassunto: Introduces both the fundamentals of time dependent differential equations and their numerical solutions Introduction to Numerical Methods for Time Dependent Differential Equations delves into the underlying mathematical theory needed to solve time dependent differential equations numerically. Written as a self-contained introduction, the book is divided into two parts to emphasize both ordinary differential equations (ODEs) and partial differential equations (PDEs). Beginning with ODEs and their approximations, the authors provide a crucial presentation of fundamen
• Titolo autorizzato: Introduction to numerical methods for time dependent differential equations
• ISBN: 1-118-83890-4; 1-118-83891-2
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910464288703321
• Lo trovi qui: Univ. Federico II