1986年张炳根给出了关于一阶时滞差分微分方程(RDDE) x(t)+sum from i=1 to n p_ix(t—τ_1)=0(P_i,τ_i,均为正、实常数,i=1,2,…,n)所有解均振动的充分性条件,本文指出,该条件实际上是充分必要条件;本文还指出,在某些条件下,该充分条...1986年张炳根给出了关于一阶时滞差分微分方程(RDDE) x(t)+sum from i=1 to n p_ix(t—τ_1)=0(P_i,τ_i,均为正、实常数,i=1,2,…,n)所有解均振动的充分性条件,本文指出,该条件实际上是充分必要条件;本文还指出,在某些条件下,该充分条件中的不等式改为等式时也是方程振动的充分必要条件。展开更多
Adaptive grid methods are established as valuable computational technique in approximating effectively the solutions of problems with boundary or interior layers. In this paper,we present the analysis of an upwind sch...Adaptive grid methods are established as valuable computational technique in approximating effectively the solutions of problems with boundary or interior layers. In this paper,we present the analysis of an upwind scheme for singularly perturbed differential-difference equation on a grid which is formed by equidistributing arc-length monitor function.It is shown that the discrete solution obtained converges uniformly with respect to the perturbation parameter.Numerical experiments illustrate in practice the result of convergence proved theoretically.展开更多
文摘1986年张炳根给出了关于一阶时滞差分微分方程(RDDE) x(t)+sum from i=1 to n p_ix(t—τ_1)=0(P_i,τ_i,均为正、实常数,i=1,2,…,n)所有解均振动的充分性条件,本文指出,该条件实际上是充分必要条件;本文还指出,在某些条件下,该充分条件中的不等式改为等式时也是方程振动的充分必要条件。
基金supported by the Department of Science & Technology, Government of India under research grant SR/S4/MS:318/06.
文摘Adaptive grid methods are established as valuable computational technique in approximating effectively the solutions of problems with boundary or interior layers. In this paper,we present the analysis of an upwind scheme for singularly perturbed differential-difference equation on a grid which is formed by equidistributing arc-length monitor function.It is shown that the discrete solution obtained converges uniformly with respect to the perturbation parameter.Numerical experiments illustrate in practice the result of convergence proved theoretically.
