| 延迟微分方程并行算法的收敛定理 |
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| 引用本文： | 丁效华,耿党辉. 延迟微分方程并行算法的收敛定理[J]. 黑龙江大学自然科学学报, 2004, 21(1): 17-22 |
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| 作者姓名： | 丁效华 耿党辉 |
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| 作者单位： | 哈尔滨工业大学,威海,数学系,山东,威海,264209;哈尔滨工业大学,威海,数学系,山东,威海,264209 |
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| 基金项目： | Supposed by the National Science Foundation of China(10271036)，Grant of HIT(Weihai)(2003-3-14,15) |
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| 摘 要： | 用Runge-Kutta法求解微分方程,数值方法有高精度和强稳定性.用来求解Runge-Kutta方程的迭代法需要很大的计算量.一种选择是在t轴的步点上应用并行迭代法.针对延迟微分方程分析了一类特殊的并行迭代法的收敛性,数值算例表明这种算法是有效的.
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| 关 键 词： | Runge-Kutta法 步并行迭代 延迟微分方程 |
The convergence theorem of parallel Runge-Kutta methods for delay differential equation |
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| Abstract. The convergence theorem of parallel Runge-Kutta methods for delay differential equation[J]. Journal of Natural Science of Heilongjiang University, 2004, 21(1): 17-22 |
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| Authors: | Abstract |
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| Abstract: | Using implicit Runge -Kutta method to solve differential equations requires that the numerical scheme have high accuracy and high stability. But, the iterative scheme needed for solving the implicit RK equations requires a lot of computational effort. One option is the application of the iteration scheme concurrently at a number of step points on the t - axis. It is necessary to analyze the convergence of a special class of such step - parallel iteration methods for delay differential equations (DDEs). |
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| Keywords: | Runge-Kutta method step - parallel iteration delay differential equation |
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