These paired vectors also reflect another important property of symplectic spaces, their intrinsic connection to complex numbers. These numbers involve i, the square root of −1, and they take the form ...

Properties of symplectic Runge-Kutta (RK) methods and symplectic partitioned Runge-Kutta (PRK) methods with real eigenvalues are discussed in this paper. It is shown that an s stage such method can't ...

In symplectic geometry, however, there’s less in the way of conventional wisdom, which invites contention, but also creates exciting possibilities. “For me personally, what was exciting in symplectic ...

SIAM Journal on Numerical Analysis, Vol. 34, No. 5 (Oct., 1997), pp. 1742-1760 (19 pages) We analyze three finite difference approximations of the nonlinear Klein-Gordon equation and show that they ...

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