G-symplectic second derivative general linear methods for Hamiltonian problems
نویسندگان
چکیده
منابع مشابه
Sequential second derivative general linear methods for stiff systems
Second derivative general linear methods (SGLMs) as an extension of general linear methods (GLMs) have been introduced to improve the stability and accuracy properties of GLMs. The coefficients of SGLMs are given by six matrices, instead of four matrices for GLMs, which are obtained by solving nonlinear systems of order and usually Runge--Kutta stability conditions. In this p...
متن کاملsequential second derivative general linear methods for stiff systems
second derivative general linear methods (sglms) as an extension of general linear methods (glms) have been introduced to improve the stability and accuracy properties of glms. the coefficients of sglms are given by six matrices, instead of four matrices for glms, which are obtained by solving nonlinear systems of order and usually runge--kutta stability conditions. in this p...
متن کاملSequential Second Derivative General Linear Methods for Stiff Systems
Second derivative general linear methods (SGLMs) as an extension of general linear methods (GLMs) have been introduced to improve the stability and accuracy properties of GLMs. The coefficients of SGLMs are given by six matrices, instead of four matrices for GLMs, which are obtained by solving nonlinear systems of order and usually Runge–Kutta stability conditions. In this paper, we introduce a...
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Numerical methods for solving weakly damped Hamiltonian systems are constructed using the popular Störmer-Verlet and implicit midpoint methods. Each method is shown to preserve dissipation of symplecticity and dissipation of angular momentum of an N -body system with pairwise distance dependent interactions. Necessary and sufficient conditions for second order accuracy are derived. Analysis for...
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The non-linear wave equation is taken as a model problem for the investigation. Different multisymplectic reformulations of the equation are discussed. Multi-symplectic Runge–Kutta methods and multi-symplectic partitioned Runge–Kutta methods are explored based on these different reformulations. Some popular and efficient multi-symplectic schemes are collected and constructed. Stability analyses...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2017
ISSN: 0377-0427
DOI: 10.1016/j.cam.2016.10.011