Diagonally Implicit Symplectic Runge-Kutta Methods with High Algebraic and Dispersion Order

The numerical integration of Hamiltonian systems with oscillating solutions is considered in this paper. A diagonally implicit symplectic nine-stages Runge-Kutta method with algebraic order 6 and dispersion order 8 is presented. Numerical experiments with some Hamiltonian oscillatory problems are presented to show the proposed method is as competitive as the existing same type Runge-Kutta methods.

Semi Implicit Hybrid Methods with Higher Order Dispersion for Solving Oscillatory Problems

We constructed three two-step semi-implicit hybrid methods (SIHMs) for solving oscillatory second order ordinary differential equations (ODEs). The first two methods are three-stage fourth-order and three-stage fifth-order with dispersion order six and zero dissipation. The third is a four-stage fifth-order method with dispersion order eight and dissipation order five. Numerical results show that SIHMs are more accurate as compared to the existing hybrid methods, Runge-Kutta Nyström (RKN) and Runge-Kutta (RK) methods of the same order and Diagonally Implicit Runge-Kutta Nyström (DIRKN) method of the same stage. The intervals of absolute stability or periodicity of SIHM for ODE are also presented.

MULTIVARIATE DISPERSION ORDER AND THE NOTION OF COPULA APPLIED TO THE MULTIVARIATE t-DISTRIBUTION

We study the concept of multivariate dispersion order, defined as the existence of an expansion function that maps a random vector to another one, for multivariate distributions with the same dependence structure. As a particular case, we can order the multivariate t-distribution family in dispersion sense. Finally, we use these results in the problem of detection and characterization of influential observations in regression analysis. This problem can often be used to compare two multivariate t-distributions.

AN AGING CONCEPT BASED ON MAJORIZATION

In this article, we introduce a new dispersion order weaker than the classic dispersion order discussed by Lewis and Thompson (1981). We study the equivalence of this order with the majorization order under the assumption of unimodality. Finally, we use this equivalence to characterize the IFR aging notion for unimodal distributions by means of the notion of decreasing in randomness.