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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
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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
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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
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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
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The Numerical Solution Of Differential-Algebraic Systems By Runge-Kutta Methods
TLDR
This 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
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Exponential Integrators for Large Systems of Differential Equations
TLDR
We study 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. Expand
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On splitting methods for Schrödinger-Poisson and cubic nonlinear Schrödinger equations
  • C. Lubich
  • Mathematics, Computer Science
  • Math. Comput.
  • 19 February 2008
TLDR
We give an error analysis of Strang-type splitting integrators for nonlinear Schrodinger equations using Lie-commutator bounds for estimating the local error and conditional stability for error propagation. Expand
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Convolution quadrature and discretized operational calculus. II
SummaryOperational quadrature rules are applied to problems in numerical integration and the numerical solution of integral equations: singular integrals (power and logarithmic singularities, finiteExpand
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Geometric numerical integration illustrated by the Störmer-Verlet method
The subject of geometric numerical integration deals with numerical integrators that preserve geometric properties of the flow of a differential equation, and it explains how structure preservationExpand
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