Research of adaptive algorithm for numerical calculation of nonlinear partial differential equations

Computer Engineering and Applications ›› 2011, Vol. 47 ›› Issue (20): 38-40.

• 研究、探讨 • Previous Articles Next Articles

Research of adaptive algorithm for numerical calculation of nonlinear partial differential equations

ZHOU Hongyu，WANG Aimin

School of Computer and Information Engineering，Anyang Normal University，Anyang，Henan 455002，China

Received:1900-01-01 Revised:1900-01-01 Online:2011-07-11 Published:2011-07-11

非线性偏微分方程数值求解的自适应方法研究

周宏宇，王爱民

安阳师范学院计算机与信息工程学院，河南安阳 455002

Abstract

Abstract: In the foundation of thorough studies on wavelet theory and its applications in numerical solution of partial differential equation，a adaptive wavelet algorithm for numerical solution of partial differential equation—wavelet optimized finite difference method is advanced.The nonlinear Burgers equation is taken as an example，WOFD and method of lines are used to solve it，it turns out that the WOFD has adaptability，high efficiency and feasibility.

Key words: partial differential equations, adaptability, wavelet, finite difference method, method of lines

摘要： 对小波理论在偏微分方程数值求解中的应用进行深入研究的基础上，提出了一种自适应求解非线性偏微分方程的算法——小波最优有限差分法。并以非线性Burgers方程为例，分别用小波最优有限差分法和直线法对它进行数值求解，显示了小波最优有限差分法在数值求解非线性问题时的自适应性、高效性和可行性。

关键词: 偏微分方程, 自适应, 小波, 有限差分法, 直线法

ZHOU Hongyu，WANG Aimin. Research of adaptive algorithm for numerical calculation of nonlinear partial differential equations[J]. Computer Engineering and Applications, 2011, 47(20): 38-40.

周宏宇，王爱民. 非线性偏微分方程数值求解的自适应方法研究[J]. 计算机工程与应用, 2011, 47(20): 38-40.

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Research of adaptive algorithm for numerical calculation of nonlinear partial differential equations

非线性偏微分方程数值求解的自适应方法研究

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