EFFICIENT SIXTH ORDER P-STABLE METHODS WITH MINIMAL LOCAL TRUNCATION ERROR FOR y"=f(x,y)

1. IntroductionWe consider a class of direct hybrid methods proposed in [11 for solving the second orderinitial value problemy" = f(t,y), y(0),y'(0) given (1.1)The basic method has the formandHere t. = nh and we define t.l.. = t. I aih, i = 1, 2 and n=0,1…     

解初值问题y″=g(x，y)的含参数块方法

1引言对于二阶常微分方程的初值问题y″=g(x,y),y(x_0)=y_0,y′(x_0)=y_0′,x_0(?)x(?)T(1)的数值解法的研究引起人们的广泛兴趣．对于直接积分(1),自从1976年J．D．Lambert和I．A．Waston提出二阶P-稳定方法和1978年G．Dahlquist证明P-稳定常系数线性多步方法的最高相容阶不超过2的重要结论以来,截止目前,已积累了许多高于2阶的P-稳定方法．例如,修正的Numerov方法,混合法(特殊形式RK的方法),多导法,Obrechkoff方法,显式RKN方法,单隐方法和对角隐式RKN方法等(顺便指出,文献[5,16]中所说的高阶方法的相容阶均不超过4)．所有这些方法,有些相     

解初值问题Y＇＇=g（x，y）的含参数块方法

引言 对于二阶常微分方程的初值问题 y＇＇=g（x,y）,y（x0）=y0,x0≤x≤T 的数值解法的研究引起人们的广泛兴趣．对于直接积分（1），自从1976年J．D．Lambert和I.A．waston[1]提出二阶P-稳定方法和1978年G．Dahlquist[2]证明P-稳定常系数线性多步方法的最高相容阶不超过的重要结论以来，截止目前，     

Stability properties of numerical methods for solving delay differential equations

Stability properties of numerical methods for delay differential equations are considered. Some suitable definitions for the stability of the numerical methods are included and Runge-Kutta type methods satisfying these properties are tested on a numerical example.     

P-stable models of strong kernel programs

The research community has long recognized the study of non-monotonic reasoning (NMR) as a promising approach to model features of commonsense reasoning. We study one of the semantics that are useful to formalize NMR, called the p-stable semantics. We introduce three different formats for normal programs: negative normal programs, restricted negative normal programs and strong kernel programs. These forms help to simplify the search of p-stable models of the original program. One of the main results of this paper indicates that the p-stable semantics for strong kernel programs is the same as the stable semantics. This way, all the applications based on stable semantics for those kernel programs (defined in [S. Costantini, A. Provetti, Normal forms for answer set programming, J. Theory Pract. Log. Program. 5 (2005) 747-760]) that are strong kernel programs can also be based on the p-stable semantics.     

解初值问题y"=g(x,y)的含参数块方法

1引言对于二阶常微分方程的初值问题y″=g(x,y),y(x_0)=y_0,y′(x_0)=y_0′,x_0(?)x(?)T(1)的数值解法的研究引起人们的广泛兴趣．对于直接积分(1),自从1976年J．D．Lambert和I．A．Waston提出二阶P-稳定方法和1978年G．Dahlquist证明P-稳定常系数线性多步方法的最高相容阶不超过2的重要结论以来,截止目前,已积累了许多高于2阶的P-稳定方法．例如,修正的Numerov方法,混合法(特殊形式RK的方法),多导法,Obrechkoff方法,显式RKN方法,单隐方法和对角隐式RKN方法等(顺便指出,文献[5,16]中所说的高阶方法的相容阶均不超过4)．所有这些方法,有些相     

三对角线性系统的P—稳定

本文分析了三对角线性系统的P-稳定性，得到三个关于三对角线性系统是P-稳定的充要条件．文中结论部分地回答了文［1，2］所提出的公开问题     

Symmetric multistep Obrechkoff methods with zero phase-lag for periodic initial value problems of second order differential equations

In this paper, symmetric multistep Obrechkoff methods of orders 8 and 12, involving a parameter p to solve a special class of second order initial value problems in which the first order derivative does not appear explicitly, are discussed. It is shown that the methods have zero phase-lag when p is chosen as 2π times the frequency of the given initial value problem.     

Explicit One-Step P-Stable Methods for Second Order Periodic Initial Value Problems

In this paper, we present an explicit one-step method for solving periodic initial value problems of second order ordinary differential equations. The method is P-stable, and of first algebraic order and high phase-lag order. To improve the algebraic order, we give a composition second order scheme with the proposed method and its adjoint. We report some numerical results to illustrate the efficiency of our methods.