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Geometric Numerical Integration: Structure Preserving Algorithms for Ordinary Differential Equations
Numerical methods that preserve properties of Hamiltonian systems, reversible systems, differential equations on manifolds and problems with highly oscillatory solutions are the subject of this book.Expand
Geometric Numerical Integration
The subject of this workshop was numerical methods that preserve geometric properties of the flow of an ordinary or partial differential equation. This was complemented by the question as to howExpand
Convolution quadrature and discretized operational calculus. I
SummaryNumerical methods are derived for problems in integral equations (Volterra, Wiener-Hopf equations) and numerical integration (singular integrands, multiple time-scale convolution). The basicExpand
Discretized fractional calculus
For the numerical approximation of fractional integrals $I^\alpha f(x) = \frac{1}{{\Gamma (\alpha )}}\int_0^x {(x - s)^{\alpha - 1} f(s)ds\qquad (x \geqq 0)} $ with $f(x) = x^{\beta - 1} g(x)$, gExpand
On Krylov Subspace Approximations to the Matrix Exponential Operator
Krylov subspace methods for approximating the action of matrix exponentials are analyzed in this paper. We derive error bounds via a functional calculus of Arnoldi and Lanczos methods that reducesExpand
The numerical solution of differential-algebraic systems by Runge-Kutta methods
TLDR
These lecture notes provide a self-contained and comprehensive treatment of the numerical solution of differential-algebraic systems using Runge-Kutta methods, and also extrapolation methods. Expand
Exponential Integrators for Large Systems of Differential Equations
TLDR
This work studies the numerical integration of large stiff systems of differential equations by methods that use matrix--vector products with the exponential or a related function of the Jacobian, and derives methods up to order 4 which are exact for linear constant-coefficient equations. Expand
On the multistep time discretization of linear\newline initial-boundary value problems and their boundary integral equations
Summary.Convergence estimates in terms of the data are shown for multistep methods applied to non-homogeneous linear initial-boundary value problems. Similar error bounds are derived for a new classExpand
On splitting methods for Schrödinger-Poisson and cubic nonlinear Schrödinger equations
  • C. Lubich
  • Computer Science, Mathematics
  • Math. Comput.
  • 19 February 2008
TLDR
An error analysis of Strang-type splitting integrators for nonlinear Schrodinger equations using Lie-commutator bounds for estimating the local error and H m -conditional stability for error propagation is given. Expand
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