Partitioned Runge-Kutta Methods for Separable Hamiltonian Problems
نویسندگان
چکیده
منابع مشابه
Partitioned Runge-kutta Methods for Separable Hamiltonian Problems
Separable Hamiltonian systems of differential equations have the form dp/dt = -dH/dq, dq/dt = dH/dp, with a Hamiltonian function H that satisfies H = T(p) + K(q) (T and V are respectively the kinetic and potential energies). We study the integration of these systems by means of partitioned Runge-Kutta methods, i.e., by means of methods where different Runge-Kutta tableaux are used for the p and...
متن کاملUniversity of Cambridge Numerical Analysis Reports Practical Symplectic Partitioned Runge{kutta and Runge{kutta{nystrr Om Methods Practical Symplectic Partitioned Runge{kutta and Runge{kutta{nystrr Om Methods
We present new symmetric fourth and sixth-order symplectic Partitioned Runge{ Kutta and Runge{Kutta{Nystrr om methods. We studied compositions using several extra stages, optimising the eeciency. An eeective error, E f , is deened and an extensive search is carried out using the extra parameters. The new methods have smaller values of E f than other methods found in the literature. When applied...
متن کاملSpatially Partitioned Embedded Runge-Kutta Methods
We study spatially partitioned embedded Runge–Kutta (SPERK) schemes for partial differential equations (PDEs), in which each of the component schemes is applied over a different part of the spatial domain. Such methods may be convenient for problems in which the smoothness of the solution or the magnitudes of the PDE coefficients vary strongly in space. We focus on embedded partitioned methods ...
متن کاملOn 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...
متن کاملLinear Stability of Partitioned Runge-Kutta Methods
We study the linear stability of partitioned Runge–Kutta (PRK) methods applied to linear separable Hamiltonian ODEs and to the semidiscretization of certain Hamiltonian PDEs. We extend the] by presenting simplified expressions of the trace of the stability matrix, tr Ms, for the Lobatto IIIA–IIIB family of symplectic PRK methods. By making the connection to Padé approximants and continued fract...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1993
ISSN: 0025-5718
DOI: 10.2307/2153105