Title | The Graduate Student's Guide to Numerical Analysis '98 [electronic resource] : Lecture Notes from the VIII EPSRC Summer School in Numerical Analysis / edited by Mark Ainsworth, Jeremy Levesley, Marco Marletta |
---|---|
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1999 |
Connect to | http://dx.doi.org/10.1007/978-3-662-03972-4 |
Descript | XI, 252 p. 22 illus. online resource |
A Simple Introduction to Error Estimation for Nonlinear Hyperbolic Conservation Laws -- 1 Introduction -- 2 Some Convection-Diffusion Problems -- 3 Continuous Dependence for Nonlinear Convection-Diffusion -- 4 Continuous Dependence for Nonlinear Convection -- 5 A Posteriori Error Estimates for Continuous Approximations -- 6 A Posteriori Error Estimates for Discontinuous Approximations -- 7 Concluding Remarks -- Notes on Accuracy and Stability of Algorithms in Numerical Linear Algebra -- 1 Introduction -- 2 Preliminaries -- 3 Symmetric Indefinite Systems -- 4 QR Factorization and Constrained Least Squares Problems -- 5 The Singular Value Decomposition and Jacobi's Method -- Numerical Analysis of Semilinear Parabolic Problems -- 1 The Continuous Problem -- 2 Local a Priori Error Estimates -- 3 ShadowingโFirst Approach -- 4 A Posteriori Error Estimates -- 5 ShadowingโSecond Approach -- Integration Schemes for Molecular Dynamics and Related Applications -- 1 Introduction -- 2 Newtonian Dynamics -- 3 The Leapfrog Method -- 4 Other Methods -- 5 Multiple Time Steps -- 6 Constrained Dynamics -- 7 Constant-Temperature and Constant-Pressure Ensembles -- 8 Stochastic Dynamics -- Numerical Methods for Bifurcation Problems -- 1 Introduction -- 2 Examples -- 3 Newton's Method and the Implicit Function Theorem -- 4 Computation of Solution Paths -- 5 The Computation of Fold (Turning) Points -- 6 Bifurcation from the Trivial Solution -- 7 Bifurcation in Nonlinear ODEs -- 8 Hopf Bifurcation -- Spectra and Pseudospectra -- 1 Eigenvalues -- 2 Pseudospectra -- 3 A Matrix Example -- 4 An Operator Example -- 5 History of Pseudospectra