On Multisymplecticity of Partitioned Runge–Kutta Methods
نویسندگان
چکیده
منابع مشابه
On Multisymplecticity of Partitioned Runge-Kutta Methods
Previously, it has been shown that discretising a multi-Hamiltonian PDE in space and time with partitioned Runge–Kutta methods gives rise to a system of equations that formally satisfy a discrete multisymplectic conservation law. However, these studies use the same partitioning of the variables into two partitions in both space and time. This gives rise to a large number of cases to be consider...
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Although Runge–Kutta and partitioned Runge–Kutta methods are known to formally satisfy discrete multisymplectic conservation laws when applied to multi-Hamiltonian PDEs, they do not always lead to well-defined numerical methods. We consider the case study of the nonlinear Schrödinger equation in detail, for which the previously known multisymplectic integrators are fully implicit and based on t...
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Although Runge–Kutta and partitioned Runge–Kutta methods are known to formally satisfy discrete multisymplectic conservation laws when applied to multi-Hamiltonian PDEs, they do not always lead to well-defined numerical methods. We consider the case study of the nonlinear Schrödinger equation in detail, for which the previously known multisymplectic integrators are fully implicit and based on t...
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ژورنال
عنوان ژورنال: SIAM Journal on Scientific Computing
سال: 2008
ISSN: 1064-8275,1095-7197
DOI: 10.1137/070688468