| Autore |
Kreiss H (Heinz-Otto)
|
| Pubbl/distr/stampa |
Hoboken, New Jersey : , : Wiley, , 2014
|
| Descrizione fisica |
1 online resource (314 p.)
|
| Disciplina |
515/.353
|
| Soggetto topico |
Differential equations, Partial - Numerical solutions
|
| Soggetto genere / forma |
Electronic books.
|
| ISBN |
1-118-83890-4
1-118-83891-2
|
| Formato |
Materiale a stampa  |
| Livello bibliografico |
Monografia |
| Lingua di pubblicazione |
eng
|
| 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
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| Record Nr. | UNINA-9910464288703321 |
Info
Introduction to numerical methods for time dependent differential equations / / Heinz-Otto Kreiss, Omar Eduardo Ortiz
