02408nmm 2200000 a 4500 3277 ART--2009-009 eng Calvo, M. calvo@unizar.es Approximate preservation of quadratic invariants by explicit Runge-Kutta methods 2006 mult. p The construction of new explicit Runge{Kutta methods taking into account, not only their accuracy, but also the preservation of Quadratic Invariants (QIs) is studied. An expression of the error of conservation of a QI by a Runge{Kutta method is given, and a new six{stage for- mula with classical order four and seventh order of QI{conservation is obtained by choosing their coe±cients so that they minimize both local and conservation errors. This formula, as well as other ones derived by Aubry and Chartier [1] and some standard formulas, have been tested with several problems with quadratic and general invariants. It is shown that the new fourth{order explicit method preserves much better the qualitative properties of the °ow than standard fourth{ order methods at the price of two extra function evaluations per step. Furthermore, it is a practical and e±cient alternative to the standard implicit methods required for a complete preservation of QIs. Runge-Kutta Methods Quadratic Invariants Pseudo-Symplectic Methods Laburta Santamaría, María Pilar laburta@unizar.es Montijano, Juan I. monti@unizar.es Rández, Luis randez@unizar.es teresa@unizar.es http://zaguan.unizar.es/record/3277/files/ART--2009-009.pdf Texto completo oai:zaguan.unizar.es:3277 driver Matemática Aplicada ART ANyA technical_report private