| 解初值问题y″=g(x，y)的含参数块方法 |
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| 引用本文： | 黄永东,赵双锁,程正兴.解初值问题y″=g(x，y)的含参数块方法[J].高等学校计算数学学报,2006(3). |
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| 作者姓名： | 黄永东 赵双锁 程正兴 |
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| 作者单位： | 西安交通大学理学院，西北第二民族学院信息与计算科学系，西安交通大学理学院 西安710049／西北第二民族学院信息与计算科学系，银川750021，银川750021，西安710049 |
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| 基金项目： | 国家民委重点科研基金资助项目，西北第二民族学院科研资助项目(2002Y023)． |
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| 摘 要： | 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
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THE BLOCK METHODS WITH A PARAMETER FOR SOLVING INITIAL VALUE PROBLEMS OF y"=g(x,y) |
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| Huang Yongdong School of Sciences,Xi'an Jiaotong University,Xi'an.THE BLOCK METHODS WITH A PARAMETER FOR SOLVING INITIAL VALUE PROBLEMS OF y"=g(x,y)[J].Numerical Mathematics A Journal of Chinese Universities,2006(3). |
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| Authors: | Huang Yongdong School of Sciences Xi'an Jiaotong University Xi'an |
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| Institution: | Huang Yongdong School of Sciences,Xi'an Jiaotong University,Xi'an 710049 Department of Mathematics,Northwest Secondly National College,Yinchuan,750021 Zhao Shuangsuo |
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| Abstract: | In this paper,we construct a class of block methods with a parameter for solving initial value problems of form y"=g(x,y).The class of block methods have some advantages:the consistency order of the r-stage explicit block methods is more than 2r,the consistency order of the r-stage implicit block methods is more than 3r;the r-stage implicit and explicit block methods are P-stable.Finally ,numerical tests show that our methods are efficient. |
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| Keywords: | Initial value problem of second order differential equations block method with a parameter P-stable consistency-order PECE scheme |
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