| ACCELERATION METHODS OF NONLINEAR ITERATION FOR NONLINEAR PARABOLIC EQUATIONS |
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| 作者姓名： | Guang-wei Yuan Xu-deng Hang |
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| 作者单位： | Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, P.O.Box 8009, Beijing 100088, China |
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| 基金项目： | Supported by the The National Basic Research Program （No. 2005CB321703） and the National Natural Science Foundation of China （No.10476002, 60533020）. |
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| 摘 要： | This paper discusses the accelerating of nonlinear parabolic equations. Two iterative methods for solving the implicit scheme new nonlinear iterative methods named by the implicit-explicit quasi-Newton （IEQN） method and the derivative free implicit-explicit quasi-Newton （DFIEQN） method are introduced, in which the resulting linear equations from the linearization can preserve the parabolic characteristics of the original partial differential equations. It is proved that the iterative sequence of the iteration method can converge to the solution of the implicit scheme quadratically. Moreover, compared with the Jacobian Free Newton-Krylov （JFNK） method, the DFIEQN method has some advantages, e.g., its implementation is easy, and it gives a linear algebraic system with an explicit coefficient matrix, so that the linear （inner） iteration is not restricted to the Krylov method. Computational results by the IEQN, DFIEQN, JFNK and Picard iteration methods are presented in confirmation of the theory and comparison of the performance of these methods.
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| 关 键 词： | 非线性抛物线方程 误差图解 牛顿迭代法 计算数学 |
| 收稿时间： | 2006-03-01 |
| 修稿时间： | 2006-03-01 |
ACCELERATION METHODS OF NONLINEAR ITERATION FOR NONLINEAR PARABOLIC EQUATIONS |
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| Guang-wei Yuan Xu-deng Hang.ACCELERATION METHODS OF NONLINEAR ITERATION FOR NONLINEAR PARABOLIC EQUATIONS[J].Journal of Computational Mathematics,2006,24(3):412-424. |
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| Authors: | Guang-wei;Yuan;Xu-deng;Hang |
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| Abstract: | This paper discusses the accelerating iterative methods for solving the implicit scheme of nonlinear parabolic equations. Two new nonlinear iterative methods named by the implicit-explicit quasi-Newton (IEQN) method and the derivative free implicit-explicit quasi-Newton (DFIEQN) method are introduced, in which the resulting linear equations from the linearization can preserve the parabolic characteristics of the original partial dif- ferential equations. It is proved that the iterative sequence of the iteration method can converge to the solution of the implicit scheme quadratically. Moreover, compared with the Jacobian Free Newton-Krylov (JFNK) method, the DFIEQN method has some ad- vantages, e. g., its implementation is easy, and it gives a linear algebraic system with an explicit coefficient matrix, so that the linear (inner) iteration is not restricted to the Krylov method. Computational results by the IEQN, DFIEQN, JFNK and Picard iteration meth- ods are presented in confirmation of the theory and comparison of the performance of these methods. |
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| Keywords: | Nonlinear parabolic equations Difference scheme Newton iterative methods |
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