Fillet,Filet
发表于 2025-3-25 05:42:04
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cluster
发表于 2025-3-25 07:28:54
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同谋
发表于 2025-3-25 12:26:50
Effective Methods for Highly Oscillatory Second-Order Nonlinear Differential Equations, procedure. When applied to Duffing’s equation for different frequencies, this waveform relaxation-asymptotic method (WRAM) is shown to be very effective. The higher the frequency is, the more accurate it is.
粗语
发表于 2025-3-25 18:25:38
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刺耳
发表于 2025-3-25 20:47:02
ant development of rooted-tree and B-series theories with ap.Structure-Preserving Algorithms for Oscillatory Differential Equations. describes a large number of highly effective and efficient structure-preserving algorithms for second-order oscillatory differential equations by using theoretical ana
细节
发表于 2025-3-26 02:43:51
Book 2013ng algorithms for second-order oscillatory differential equations by using theoretical analysis and numerical validation. Structure-preserving algorithms for differential equations, especially for oscillatory differential equations, play an important role in the accurate simulation of oscillatory pr
Herd-Immunity
发表于 2025-3-26 06:27:12
,Runge–Kutta (–Nyström) Methods for Oscillatory Differential Equations,. For first-order differential equations, Runge–Kutta (RK) methods are presented. For the purpose of deriving order conditions, the rooted tree theory is set up. For second-order differential equations, Runge–Kutta–Nyström (RKN) methods are formulated, and their order conditions are obtained based o
珍奇
发表于 2025-3-26 09:02:02
ARKN Methods,l equations .″+...=.(.,.′), where .>0 is the main frequency. Based on the internal stages of the traditional RKN methods, ARKN methods adopt a new form of updates which incorporate the special oscillatory structure of the system. Order conditions for ARKN methods are derived by means of the Nyström
租约
发表于 2025-3-26 15:51:05
ERKN Methods, matrix . is positive semi-definite. ERKN methods make full use of the special structure of the equation introduced by the linear term . so that they are exact in both the internal stages and the updates when applied to the multidimensional homogeneous system .″+.=.. In order to derive the order con
DALLY
发表于 2025-3-26 20:38:42
Symplectic and Symmetric Multidimensional ERKN Methods,ms. Chapter 4 focuses on the investigation of symplectic and symmetric multi-frequency and multidimensional extended Runge–Kutta–Nyström (SSMERKN) integrators. The symplecticity and symmetry conditions for multidimensional ERKN methods are obtained. When the principal frequency matrix vanishes, they