Hormones
发表于 2025-3-27 00:59:45
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Coordinate
发表于 2025-3-27 02:37:18
Conservation of First Integrals and Methods on Manifolds,n manifolds. Our investigation will follow two directions. We first investigate which of the methods introduced in Chap. II conserve invariants automatically. We shall see that most of them conserve linear invariants, a few of them quadratic invariants, and none of them conserves cubic or general no
BLANK
发表于 2025-3-27 07:57:44
Symmetric Integration and Reversibility,s. We discuss reversible differential equations and reversible maps, and we explain how symmetric integrators are related to them. We study symmetric Runge–Kutta and composition methods, and we show how standard approaches for solving differential equations on manifolds can be symmetrized. A theoret
明确
发表于 2025-3-27 12:34:46
Structure-Preserving Implementation,not deteriorate the correct qualitative behaviour of the solution.We study multiple time stepping strategies, the effect of round-off in long-time integrations, and the efficient solution of nonlinear systems arising in implicit integration schemes.
外貌
发表于 2025-3-27 16:17:14
Hamiltonian Perturbation Theory and Symplectic Integrators, in what is for the theoretician a rather disappointing way. With modern calculating machines, one is now able to compute directly results even more accurately than those provided by perturbation theory.
Unsaturated-Fat
发表于 2025-3-27 21:02:10
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Debrief
发表于 2025-3-27 23:38:14
Dissipatively Perturbed Hamiltonian and Reversible Systems,ame is true for symmetric methods applied to non-reversible perturbations of reversible systems. In this chapter we study the behaviour of numerical integrators when they are applied to dissipative perturbations of integrable systems, where only one invariant torus persists under the perturbation an
HAWK
发表于 2025-3-28 05:29:49
Oscillatory Differential Equations with Constant High Frequencies,new complete function evaluation only after a time step over one or many periods of the fastest oscillations in the system. Various such methods have been proposed in the literature – some of them decades ago, some very recently, motivated by problems from molecular dynamics, astrophysics and nonlin
BROOK
发表于 2025-3-28 09:13:42
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强化
发表于 2025-3-28 11:18:23
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