| A PARALLEL COMPUTATION SCHEME FOR IMPLICIT RUNGE-KUTTA METHODS AND THE ITERATIVELY B-CONVERGENCE OF ITS NEWTON ITERATIVE PROCESS |
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| 作者姓名： | 赵双锁 王昌银 |
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| 作者单位： | Zhao Shuang-suo Department of Mathematics，Lanzhou University，Lanzhou，730000，PRC.Wang Chang-yin Department of Mathematics，Lanzhou University，Lanzhou，730000，PRC. |
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| 基金项目： | national natural science foundation，natural science foundation of Gansu province. |
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| 摘 要： | In this paper, based on the implicit Runge-Kutta(IRK) methods, we derive a class of parallel scheme that can be implemented on the parallel computers with Ns(N is a positive even number) processors efficiently, and discuss the iteratively B-convergence of the Newton iterative process for solving the algebraic equations of the scheme, secondly we present a strategy providing initial values parallelly for the iterative process. Finally, some numerical results show that our parallel scheme is higher efficient as N is not so large.
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A PARALLEL COMPUTATION SCHEME FOR IMPLICIT RUNGE-KUTTA METHODS AND THE ITERATIVELY B-CONVERGENCE OF ITS NEWTON ITERATIVE PROCESS |
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| Zhao Shuang-suo.A PARALLEL COMPUTATION SCHEME FOR IMPLICIT RUNGE-KUTTA METHODS AND THE ITERATIVELY B-CONVERGENCE OF ITS NEWTON ITERATIVE PROCESS[J].Numerical Mathematics A Journal of Chinese Universities English Series,1994(1). |
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| Authors: | Zhao Shuang-suo |
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| Institution: | Zhao Shuang-suo Department of Mathematics,Lanzhou University,Lanzhou,730000,PRC.Wang Chang-yin Department of Mathematics,Lanzhou University,Lanzhou,730000,PRC. |
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| Abstract: | In this paper, based on the implicit Runge-Kutta(IRK) methods, we derive a class of parallel scheme that can be implemented on the parallel computers with Ns(N is a positive even number) processors efficiently, and discuss the iteratively B-convergence of the Newton iterative process for solving the algebraic equations of the scheme, secondly we present a strategy providing initial values parallelly for the iterative process. Finally, some numerical results show that our parallel scheme is higher efficient as N is not so large. |
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| Keywords: | Implicit Range-Kutta methods Newton iterative process parallel computation iteratively B-convergence |
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