This paper presents a class of r-point (r+1)st-order A-stable one-block methods with damping at the infinite point (DIAOB r,r+1 ). Under the conditions of the same order, A-stability, operation count (at each iterativ...This paper presents a class of r-point (r+1)st-order A-stable one-block methods with damping at the infinite point (DIAOB r,r+1 ). Under the conditions of the same order, A-stability, operation count (at each iterative step) and storage space are the same as the methods in , the methods in the paper improve the stability in a neighborhood at the infinite point. And, by using the OOPI method , it possesses much faster rate of convergence for solving systems of nonlinear equations produced by the DIAOB r,r+1 .展开更多
This paper is concerned with a delay differential equationx=-x + f(y(t-r)), y=-y-f(x(t-r)),where delay r is a positive constant, and f is a signal transmission function of McCulloch-Pitts type.We obtain some sufficien...This paper is concerned with a delay differential equationx=-x + f(y(t-r)), y=-y-f(x(t-r)),where delay r is a positive constant, and f is a signal transmission function of McCulloch-Pitts type.We obtain some sufficient and necessary conditions for the asymptotic behavior of network (*) with σ ≤-1 .The results obtained show that the large time behaviors of solutions of (*) are dependent of r if σ= -1. These results improve the corresponding theorems in [3] by removing the restriction of the initial conditions.展开更多
文摘This paper presents a class of r-point (r+1)st-order A-stable one-block methods with damping at the infinite point (DIAOB r,r+1 ). Under the conditions of the same order, A-stability, operation count (at each iterative step) and storage space are the same as the methods in , the methods in the paper improve the stability in a neighborhood at the infinite point. And, by using the OOPI method , it possesses much faster rate of convergence for solving systems of nonlinear equations produced by the DIAOB r,r+1 .
文摘This paper is concerned with a delay differential equationx=-x + f(y(t-r)), y=-y-f(x(t-r)),where delay r is a positive constant, and f is a signal transmission function of McCulloch-Pitts type.We obtain some sufficient and necessary conditions for the asymptotic behavior of network (*) with σ ≤-1 .The results obtained show that the large time behaviors of solutions of (*) are dependent of r if σ= -1. These results improve the corresponding theorems in [3] by removing the restriction of the initial conditions.
