Orthosymplectic integration of linear Hamiltonian systems
A continuous, orthogonal and symplectic factorization procedure for integrating unstable linear Hamiltonian systems is presented. The method is based on the development of an orthogonal, symplectic change of variables to block triangular Hamiltonian form. Integration is thus carried out within the class of linear Hamiltonian systems. Use of an appropriate timestepping strategy ensures that the symplectic pairing of eigenvalues is automatically preserved. For long-term integrations, which are necessary in the calculation of Lyapunov exponents, the properties of such a symplectic framework can be expected to yield improved estimates. The method is illustrated and compared with other techniques by means of numerical experiments on some equations.
scientific article; zbMATH DE number 1049545