Numerical Solution of Boundary Value Problems for Ordinary Differential Equations - Brossura

Ascher, Uri M.; Mattheij, Robert M. M.; Russell, Robert D.

 
9780898713541: Numerical Solution of Boundary Value Problems for Ordinary Differential Equations
Brossura
ISBN 10: 0898713544 ISBN 13: 9780898713541
Casa editrice: Society for Industrial and Applied Mathematics, 1995

Sinossi

The most comprehensive, up to date account of the popular numerical methods for solving boundary value problems in ODEs.

Le informazioni nella sezione "Riassunto" possono far riferimento a edizioni diverse di questo titolo.

Descrizione del libro

The most comprehensive, up to date account of the popular numerical methods for solving boundary value problems in ordinary differential equations. It aims at a thorough understanding of the field by giving an in-depth analysis of the numerical methods by using decoupling principles.

Contenuti

List of Examples; Preface; 1. Introduction. Boundary Value Problems for Ordinary Differential Equations; Boundary Value Problems in Applications; 2. Review of Numerical Analysis and Mathematical Background. Errors in Computation; Numerical Linear Algebra; Nonlinear Equations; Polynomial Interpolation; Piecewise Polynomials, or Splines; Numerical Quadrature; Initial Value Ordinary Differential Equations; Differential Operators and Their Discretizations; 3. Theory of Ordinary Differential Equations. Existence and Uniqueness Results; Green's Functions; Stability of Initial Value Problems; Conditioning of Boundary Value Problems; 4. Initial Value Methods. Introduction. Shooting; Superposition and Reduced Superposition; Multiple Shooting for Linear Problems; Marching Techniques for Multiple Shooting; The Riccati Method; Nonlinear Problems; 5. Finite Difference Methods. Introduction; Consistency, Stability, and Convergence; Higher-Order One-Step Schemes; Collocation Theory; Acceleration Techniques; Higher-Order ODEs; Finite Element Methods; 6. Decoupling. Decomposition of Vectors; Decoupling of the ODE; Decoupling of One-Step Recursions; Practical Aspects of Consistency; Closure and Its Implications; 7. Solving Linear Equations. General Staircase Matrices and Condensation; Algorithms for the Separated BC Case; Stability for Block Methods; Decomposition in the Nonseparated BC Case; Solution in More General Cases; 8. Solving Nonlinear Equations. Improving the Local Convergence of Newton's Method; Reducing the Cost of the Newton Iteration; Finding a Good Initial Guess; Further Remarks on Discrete Nonlinear BVPS; 9. Mesh Selection. Introduction; Direct Methods; A Mesh Strategy for Collocation; Transformation Methods; General Considerations; 10. Singular Perturbations. Analytical Approaches; Numerical Approaches; Difference Methods; Initial Value Methods; 11. Special Topics. Reformulation of Problems in 'Standard' Form; Generalized ODEs and Differential Algebraic Equations; Eigenvalue Problems; BVPs with Singularities; Infinite Intervals; Path Following, Singular Points and Bifurcation; Highly Oscillatory Solutions; Functional Differential Equations; Method of Lines for PDEs; Multipoint Problems; On Code Design and Comparison; Appendix A. A Multiple Shooting Code; Appendix B. A Collocation Code; References; Bibliography; Index.

Le informazioni nella sezione "Su questo libro" possono far riferimento a edizioni diverse di questo titolo.

Editore
Society for Industrial and Applied Mathematics
Data di pubblicazione
1995
Lingua
Inglese
ISBN 10 
0898713544
ISBN 13 
9780898713541
Rilegatura
Copertina flessibile
Numero di pagine
621
Contatto del produttore
non disponibile
Persona responsabile
Buchpark GmbH
gpsr@buchpark.de

Krügerweg 1
Trebbin
Brandenburg
14959
Germania

Altre edizioni note dello stesso titolo

9780136272663: Numerical Solution of Boundary Value Problems for Ordinary Differential Equations

Edizione in evidenza

ISBN 10:  0136272665 ISBN 13:  9780136272663
Casa editrice: Prentice Hall, 1988
Rilegato