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Cited by 50 publications
(63 citation statements)
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“…Consequently, we notice that one needs only to compute once and for all matrix Σ (or factorize Σ −1 ), having the same size as that of the continuous problem. Secondly, in order to gain convergence for relatively large values of ωh, it is important to choose an appropriate starting value ψ 0 in (47). For this purpose, we use the solution of the associated homogeneous problem (14).…”
Section: Efficient Implementation Of the Methodsmentioning
confidence: 99%
“…Consequently, we notice that one needs only to compute once and for all matrix Σ (or factorize Σ −1 ), having the same size as that of the continuous problem. Secondly, in order to gain convergence for relatively large values of ωh, it is important to choose an appropriate starting value ψ 0 in (47). For this purpose, we use the solution of the associated homogeneous problem (14).…”
Section: Efficient Implementation Of the Methodsmentioning
confidence: 99%
“…In addition, continuous-stage approaches may promote the investigation of conjugate symplecticity of energy-preserving methods [16,17,32]. Besides, as shown in [30,34,35], some Galerkin variational methods can be interpreted as continuous-stage (P)RK methods, but they can not be clearly understood in the classical (P)RK framework. Therefore, the concept of continuous-stage methods provides us a larger realm for numerical discretization of differential equations and it opens a new insight for us in geometric integration.…”
Section: Introductionmentioning
confidence: 99%
“…For non-polynomial cases, a practical energy-preserving scheme is usually gained in the sense that the energy error remains bounded within machine precision, but one has to increase RK stages [2]. Recently, energy-preserving continuous stage RK (CSRK) methods have been attracting a lot of interest [21,30,33,38]. This kind of methods can eliminate the limit of HBVMs to cover non-polynomial Hamiltonian systems.…”
Section: Introductionmentioning
confidence: 99%