The graduate student's guide to numerical analysis '98 : lecture notes from the VIII EPSRC Summer School in Numerical Analysis
著者
書誌事項
The graduate student's guide to numerical analysis '98 : lecture notes from the VIII EPSRC Summer School in Numerical Analysis
(Springer series in computational mathematics, 26)
Springer, c1999
大学図書館所蔵 全29件
  青森
  岩手
  宮城
  秋田
  山形
  福島
  茨城
  栃木
  群馬
  埼玉
  千葉
  東京
  神奈川
  新潟
  富山
  石川
  福井
  山梨
  長野
  岐阜
  静岡
  愛知
  三重
  滋賀
  京都
  大阪
  兵庫
  奈良
  和歌山
  鳥取
  島根
  岡山
  広島
  山口
  徳島
  香川
  愛媛
  高知
  福岡
  佐賀
  長崎
  熊本
  大分
  宮崎
  鹿児島
  沖縄
  韓国
  中国
  タイ
  イギリス
  ドイツ
  スイス
  フランス
  ベルギー
  オランダ
  スウェーデン
  ノルウェー
  アメリカ
注記
"The Eighth EPSRC Numerical Analysis Summer School was held at the University of Leicester from the 5th to the 17th of July, 1998" -- Pref
Includes bibliographical references
内容説明・目次
内容説明
Detailed lecture notes on six topics at the forefront of current research in numerical analysis and applied mathematics, with each set of notes presenting a self-contained guide to a current research area and supplemented by an extensive bibliography. In addition, most of the notes contain detailed proofs of the key results. They start from a level suitable for first year graduates in applied mathematics, mathematical analysis or numerical analysis, and proceed to current research topics. Readers will thus quickly gain an insight into the important results and techniques in each area without recourse to the large research literature. Current (unsolved) problems are also described, and directions for future research given.
目次
A Simple Introduction to Error Estimation for Nonlinear Hyperbolic Conservation Laws.- 1 Introduction.- 2 Some Convection-Diffusion Problems.- 2.1 Traffic Flow.- 2.2 Propagation of Phase Transitions.- 2.3 Concluding Remarks.- 3 Continuous Dependence for Nonlinear Convection-Diffusion.- 3.1 The Standard Duality Technique and the Adjoint Problem.- 3.2 A Technique to Bypass the Resolution of the Adjoint Problem.- 3.3 A Very Simple Way of Handling the Convective Nonlinearity f.- 3.4 Continuous Dependence Results in L1-like Norms.- 3.5 Allowing the Diffusion Coefficients to Go to Zero.- 3.6 New Continuous Dependence Results.- 3.7 Relaxing the Smoothness in Time of the Approximate Solution u.- 3.8 The a Posteriori Error Estimate for Non-Smooth u.- 3.9 Concluding Remarks.- 4 Continuous Dependence for Nonlinear Convection.- 4.1 Existence and Uniqueness of the Entropy Solution.- 4.2 The Inherited Continuous Dependence Results.- 4.3 Concluding Remarks.- 5 A Posteriori Error Estimates for Continuous Approximations.- 5.1 The Error Estimate.- 5.2 Application to the Engquist-Osher Scheme.- 5.3 Explaining the Numerical Results.- 5.4 Another Error Estimate.- 6 A Posteriori Error Estimates for Discontinuous Approximations.- 6.1 The Case of a Finite Number of Smooth Discontinuity Curves.- 6.2 The Case of a Piecewise-Constant Approximation.- 7 Concluding Remarks.- 7.1 Some Bibliographical Remarks.- 7.2 Open Problems.- Notes on Accuracy and Stability of Algorithms in Numerical Linear Algebra.- 1 Introduction.- 2 Preliminaries.- 3 Symmetric Indefinite Systems.- 3.1 Block LDLT Factorization.- 3.2 Aasen's Method.- 3.3 Aasen's Method Versus Block LDLT Factorization.- 3.4 Tridiagonal Matrices.- 4 QR Factorization and Constrained Least Squares Problems.- 4.1 Householder QR Factorization.- 4.2 The Constrained Least Squares Problem.- 5 The Singular Value Decomposition and Jacobi's Method.- 5.1 Jacobi's Method.- 5.2 Relative Perturbation Theory.- 5.3 Error Analysis.- 5.4 Other Issues.- Numerical Analysis of Semilinear Parabolic Problems.- 1 The Continuous Problem.- 2 Local a Priori Error Estimates.- 2.1 The Spatially Semidiscrete Problem.- 2.2 A Completely Discrete Scheme.- 3 Shadowing-First Approach.- 3.1 Linearization.- 3.2 Exponential Dichotomies.- 3.3 Shadowing.- 4 A Posteriori Error Estimates.- 4.1 The Error Equation.- 4.2 Local Estimates of the Residual.- 4.3 A Global Error Estimate.- 5 Shadowing-Second Approach.- Integration Schemes for Molecular Dynamics and Related Applications.- 1 Introduction.- 2 Newtonian Dynamics.- 2.1 Properties.- 2.2 The Liouville Equation.- 3 The Leapfrog Method.- 3.1 Derivation.- 3.2 Small-?t Analysis.- 3.3 Linear Analysis.- 3.4 Small-Energy Analysis.- 3.5 Effective Accuracy and Post-Processing.- 3.6 Finite-Precision Effects.- 4 Other Methods.- 4.1 A Family of Methods.- 4.2 Quest for Accuracy and Stability.- 4.3 The Case for Symplectic Integration.- 5 Multiple Time Steps.- 5.1 The Verlet-I/r-RESPA/Impulse MTS Method.- 5.2 Partitioning of Interactions.- 5.3 Efficient Implementation.- 5.4 Mollified Impulse MTS Methods.- 6 Constrained Dynamics.- 6.1 Discretization.- 6.2 Solution of the Nonlinear Equations.- 7 Constant-Temperature and Constant-Pressure Ensembles.- 7.1 Constant-Temperature Ensembles.- 7.2 Constant-Pressure Ensembles.- 8 Stochastic Dynamics.- 8.1 Langevin Dynamics.- 8.2 Brownian Dynamics.- A Lie Series and the BCH Formula.- B Stochastic Processes.- 2.1 Wiener Processes.- 2.2 The Ito Integral.- 2.3 Stochastic Differential Equations.- 2.4 The Fokker-Planck Equation.- 2.5 The Ito Formula.- 2.6 Weak Ito-Taylor Expansions.- Numerical Methods for Bifurcation Problems.- 1 Introduction.- 2 Examples.- 3 Newton's Method and the Implicit Function Theorem.- 3.1 Newton's Method for Systems.- 3.2 The Implicit Function Theorem.- 3.3 Two Examples.- 4 Computation of Solution Paths.- 4.1 Keller's Pseudo-Arclength Continuation [25].- 4.2 Block Elimination.- 5 The Computation of Fold (Turning) Points.- 5.1 Analysis of Fold Points.- 5.2 Numerical Calculation of Fold Points.- 6 Bifurcation from the Trivial Solution.- 6.1 Scalar Case.- 6.2 n-Dimensional Case.- 7 Bifurcation in Nonlinear ODEs.- 7.1 The Shooting Method for ODEs.- 7.2 Analysis of Parameter Dependent ODEs.- 7.3 Calculation of Fold Points in ODEs Using Shooting.- 8 Hopf Bifurcation.- 8.1 Calculation of a Hopf Bifurcation Point.- 8.2 The Detection of Hopf Bifurcations in Large Systems.- Spectra and Pseudospectra.- 1 Eigenvalues.- 2 Pseudospectra.- 3 A Matrix Example.- 4 An Operator Example.- 5 History of Pseudospectra.
「Nielsen BookData」 より