| 一类求解stiff 常微分方程组非线性显式及隐式单步法 |
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| 引用本文： | 向开理.一类求解stiff 常微分方程组非线性显式及隐式单步法[J].四川师范大学学报(自然科学版),1992(4). |
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| 作者姓名： | 向开理 |
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| 作者单位： | 西南石油学院 四川南充市637001 |
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| 摘 要： | 本文构造了一类适于求解stiff 和振荡问题具A-稳定的非线性显式单步法及L-稳定的隐式单步法.这些方法与一些文献的同阶方法相比,具有相同的数值稳定性和较少的计算量.本文构造的L-稳定的数值积分公式对于特征值接近或位于虚轴的stiff 问题也是有效的.文末的数值例子表明,本文所构造的方法对某些类型的stiff 问题是有效的.
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| 关 键 词： | stiff常微分方程组 局部有理插值 高阶全导数 L-稳定 |
A CLASS OF NONLINEAR EXPLICIT AND IMPLICIT ONE-STEP METHODS FOR SOLVING STIFF SYSTEMS OF ODES |
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| Xiang Kaili.A CLASS OF NONLINEAR EXPLICIT AND IMPLICIT ONE-STEP METHODS FOR SOLVING STIFF SYSTEMS OF ODES[J].Journal of Sichuan Normal University(Natural Science),1992(4). |
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| Authors: | Xiang Kaili |
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| Abstract: | In this paper,by using a rational function to fit the theoretical solution y(x)of initial value problem,the nonlinear ex-plicit and implicit one-step methods with A-stability and L-stability are suggested respectively.These methods need no evalua-tion of the total derivatives of the function f(x,y),and have the advantage of less amount of work and good stability compar-ing with the same order methods in some literatures,which are very efficient for some stiff and highly oscillatory system ofODES in the numerical results at the end of the paper here. |
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| Keywords: | stiff ordinary differential equations local rational interpolation the total derivatives L-stability |
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