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首页> 外文期刊>American journal of applied sciences >A NON-LINEAR ABSOLUTELY-STABLE EXPLICIT NUMERICAL INTEGRATION ALGORITHM FOR STIFF INITIAL-VALUE PROBLEMS | Science Publications
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A NON-LINEAR ABSOLUTELY-STABLE EXPLICIT NUMERICAL INTEGRATION ALGORITHM FOR STIFF INITIAL-VALUE PROBLEMS | Science Publications

机译：一种非线性绝对稳定的刚性初始值问题的明确数值积分算法科学出版物

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> The time-step in integration process has two restrictions. The first one is the time step restriction due to accuracy requirement ?ac and the second one is the time-step restriction due to stability requirement ?st. The most of explicit methods have small stability regions and consequently small ?st. It obliges us to solve stiff problems with small step size ?st ?ac. The implicit methods work well with stiff problems but these methods require more work per step than the explicit methods. In this study, a non-linear absolutly stable explicit one step numerical integration algorithm is proposed for solving non linear stiff initial-value problems in ordinary differential equations. The algorithm is based on deriving a non-linear relation between the dependent variable and its derivatives from the well known Taylor expansion. The accuracy of the method depends on some unknown parameter inserted in Taylor expansion and determined from the error analysis. The accuracy and stability properties of the method are investigated and shown to yield at least third-order and A-stable. The results obtained in the numerical experiments show the efficiency of the present method in solving stiff initial value problems.
机译： >集成过程中的时间步骤有两个限制。第一个是由于精度要求的时间步骤限制？交流，第二个是由于稳定性要求引起的时间步骤限制？ st 。最明确的方法具有小的稳定性区域，因此小？ st 。它有助于我们解决小型尺寸的僵硬问题？ st ？ ac 。隐式方法适用于僵硬的问题，但这些方法每步需要比显式方法更多的工作。在该研究中，提出了一种非线性绝对稳定的一个步长数值积分算法，用于在常微分方程中解决非线性刚性初始值问题。该算法基于从已知的泰勒膨胀之间导出因变量与其衍生物之间的非线性关系。该方法的准确性取决于插入泰勒膨胀中的一些未知参数，并从误差分析中确定。研究了该方法的准确性和稳定性，并显示出至少三阶和稳定的。在数值实验中获得的结果表明了本方法解决抗初始初始值问题的效率。

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