Titlebook: Structure-Preserving Algorithms for Oscillatory Differential Equations; Xinyuan Wu,Xiong You,Bin Wang Book 2013 Science Press Beijing and

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同谋

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.

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刺耳

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

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

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,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

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

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

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