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1.

図書
図書
1. The State of the art in numerical analysis : proceedings of the Joint IMA/SIAM Conference on the State of the Art in Numerical Analysis held at the University of Birmingham, 14-18 April 1986
edited by A. Iserles and M.J.D. Powell
出版情報: Oxford [Oxfordshire] : Clarendon Press, 1987 , New York : Oxford University Press, 1987  xiv, 719 p. ; 24 cm
シリーズ名: The Institute of Mathematics and its Applications conference series ; New series ; 9
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Selections from The State of the Art in Numerical Analysis
Eigenvalue Problems / J.H. Wilkinson1：
Numerical Linear Algebra in Statistical Computing / N.J. Higham ; G.W. Stewart2：
Sparse Matrices / J.K. Reid3：
Multivariate Approximation / C. de Boor4：
Data Approximation by Splines in One and Two Independent Variables / M. Cox5：
Methods for Best Approximation and Regression Problems / G.A. Watson6：
Branch Cuts for Complex Elementary Functions / W. Kahan7：
Recent Developments in Linear and Quadratic Programming / R. Fletcher8：
Solving Systems of Non-Linear Equations by Tensor Method / R.B. Schnabel ; P.D. Frank9：
Numerical Methods for Bifurcation Problems / A.D. Jepson ; A. Spence10：
Selections from The State of the Art in Numerical Analysis
Eigenvalue Problems / J.H. Wilkinson1：
Numerical Linear Algebra in Statistical Computing / N.J. Higham ; G.W. Stewart2：
2.

図書
図書
2. The dynamics of numerics and the numerics of dynamics
edited by D.S. Broomhead and A. Iserles
出版情報: Oxford : Clarendon Press, 1992  xii, 258 p. ; 25 cm
シリーズ名: The Institute of Mathematics and its Applications conference series ; new ser. ; 34
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General Methods for Approximating Inertial Manifolds: Applications to Computing / R. Temam1：
Slowly Varying Solutions of a Nonlinear Partial Differential Equation / J. Carr2：
Bifurcation Theory Old and New / I.N. Stewart3：
The Geometry of Dynamics / D.S. Broomhead4：
Numerical Ordinary Differential Equations vs. Dynamical Systems / J.M. Sanz-Serna5：
Sensitivity of Bifurcations to Discretization / D.R. Moore ; N.O. Weiss6：
A Numerical Approach to Hilbert's Sixteenth Problem / H.B. Keller7：
Some Aspects of the Dynamics and Numerics of Hamiltonian Systems / R.S. Mackay8：
Uses and Abuses of Numerical Methods in Cardiology / J. P. Keener9：
Spurious Behaviour and Nonlinear Instability in Descretised Partial Differential Equations / D.F. Griffiths ; A.R. Mitchell10：
Dynamics and Numerics / J.K. Hale11：
General Methods for Approximating Inertial Manifolds: Applications to Computing / R. Temam1：
Slowly Varying Solutions of a Nonlinear Partial Differential Equation / J. Carr2：
Bifurcation Theory Old and New / I.N. Stewart3：
3.

図書
図書
3. A first course in the numerical analysis of differential equations. 2nd ed (: pbk)
Arieh Iserles
出版情報: Cambridge : Cambridge University Press, 2009  xviii, 459 p. ; 25 cm
シリーズ名: Cambridge texts in applied mathematics
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Preface to the second edition
Preface to the first edition
Flowchart of contents
Ordinary differential equations / I：
Euler's method and beyond / 1：
Ordinary differential equations and the Lipschitz condition / 1.1：
Euler's method / 1.2：
The trapezoidal rule / 1.3：
The theta method / 1.4：
Comments and bibliography
Exercises
Multistep methods / 2：
The Adams method / 2.1：
Order and convergence of multistep methods / 2.2：
Backward differentiation formulae / 2.3：
Runge-Kutta methods / 3：
Gaussian quadrature / 3.1：
Explicit Runge-Kutta schemes / 3.2：
Implicit Runge-Kutta schemes / 3.3：
Collocation and IRK methods / 3.4：
Stiff equations / 4：
What are stiff ODEs? / 4.1：
The linear stability domain and A-stability / 4.2：
A-stability of Runge-Kutta methods / 4.3：
A-stability of multistep methods / 4.4：
Geometric numerical integration / 5：
Between quality and quantity / 5.1：
Monotone equations and algebraic stability / 5.2：
From quadratic invariants to orthogonal flows / 5.3：
Hamiltonian systems / 5.4：
Error control / 6：
Numerical software vs. numerical mathematics / 6.1：
The Milne device / 6.2：
Embedded Runge-Kutta methods / 6.3：
Nonlinear algebraic systems / 7：
Functional iteration / 7.1：
The Newton-Raphson algorithm and its modification / 7.2：
Starting and stopping the iteration / 7.3：
The Poisson equation / II：
Finite difference schemes / 8：
Finite differences / 8.1：
The finite element method / 8.2：
Two-point boundary value problems / 9.1：
A synopsis of FEM theory / 9.2：
Spectral methods / 9.3：
Sparse matrices vs. small matrices / 10.1：
The algebra of Fourier expansions / 10.2：
The fast Fourier transform / 10.3：
Second-order elliptic PDEs / 10.4：
Chebyshev methods / 10.5：
Gaussian elimination for sparse linear equations / 11：
Banded systems / 11.1：
Graphs of matrices and perfect Cholesky factorization / 11.2：
Classical iterative methods for sparse linear equations / 12：
Linear one-step stationary schemes / 12.1：
Classical iterative methods / 12.2：
Convergence of successive over-relaxation / 12.3：
Multigrid techniques / 12.4：
In lieu of a justification / 13.1：
The basic multigrid technique / 13.2：
The full multigrid technique / 13.3：
Poisson by multigrid / 13.4：
Conjugate gradients / 14：
Steepest, but slow, descent / 14.1：
The method of conjugate gradients / 14.2：
Krylov subspaces and preconditioners / 14.3：
Poisson by conjugate gradients / 14.4：
Fast Poisson solvers / 15：
TST matrices and the Hockney method / 15.1：
Fast Poisson solver in a disc / 15.2：
Partial differential equations of evolution / III：
The diffusion equation / 16：
A simple numerical method / 16.1：
Order, stability and convergence / 16.2：
Numerical schemes for the diffusion equation / 16.3：
Stability analysis I: Eigenvalue techniques / 16.4：
Stability analysis II: Fourier techniques / 16.5：
Splitting / 16.6：
Hyperbolic equations / 17：
Why the advection equation? / 17.1：
Finite differences for the advection equation / 17.2：
The energy method / 17.3：
The wave equation / 17.4：
The Burgers equation / 17.5：
Appendix Bluffer's guide to useful mathematics
Linear algebra / A.1：
Vector spaces / A.1.1：
Matrices / A.1.2：
Inner products and norms / A.1.3：
Linear systems / A.1.4：
Eigenvalues and eigenvectors / A.1.5：
Bibliography
Analysis / A.2：
Introduction to functional analysis / A.2.1：
Approximation theory / A.2.2：
Index / A.2.3：
Preface to the second edition
Preface to the first edition
Flowchart of contents
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