Let M be a compact m-dimensional Riemannian manifold,let d denote its diameter,-R(R>0) the lower bound of the Ricci curvature,and λ1 the first eigenvalue for the Laplacian on M.Then there ex-ists a constant Cm=ma...Let M be a compact m-dimensional Riemannian manifold,let d denote its diameter,-R(R>0) the lower bound of the Ricci curvature,and λ1 the first eigenvalue for the Laplacian on M.Then there ex-ists a constant Cm=max｛√m-1,√2｝,such that λ1≥π^2/d^2·1/(2-11/2π^2)+11/2π^2e^Cm√Rd^2.展开更多
This paper deals with the parallel diagonal implicit Runge-Kutta methods for solving DDEs with a constant delay. It is shown that the suitable choice of the predictor matrix can guarantee the stability of the methods....This paper deals with the parallel diagonal implicit Runge-Kutta methods for solving DDEs with a constant delay. It is shown that the suitable choice of the predictor matrix can guarantee the stability of the methods. It is proved that for the suitable selection of the diagonal matrix D, the method based on Radau IIA is δ-convergent, and the estimates for the non-stiff speed and the stiff speed of convergence are given.展开更多
文摘Let M be a compact m-dimensional Riemannian manifold,let d denote its diameter,-R(R>0) the lower bound of the Ricci curvature,and λ1 the first eigenvalue for the Laplacian on M.Then there ex-ists a constant Cm=max｛√m-1,√2｝,such that λ1≥π^2/d^2·1/(2-11/2π^2)+11/2π^2e^Cm√Rd^2.
文摘This paper deals with the parallel diagonal implicit Runge-Kutta methods for solving DDEs with a constant delay. It is shown that the suitable choice of the predictor matrix can guarantee the stability of the methods. It is proved that for the suitable selection of the diagonal matrix D, the method based on Radau IIA is δ-convergent, and the estimates for the non-stiff speed and the stiff speed of convergence are given.
