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常微分方程特征值问题求解器解法的改进 被引量:4

THE IMPROVEMENT OF ODE SOLVER METHOD IN THE ANALYSIS OF ODE EIGENVALUE PROBLEM
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摘要 对于工程中的常微分方程(ODE)特征值问题,已有一套完整的算法,并据此算法开发出ODE特征值求解程序COLEGN。该程序需要用户输入直接求解(非线性)和逆幂迭代(线性)两套ODE体系,输入繁琐,不便于使用。针对这一问题,研究了这两套ODE体系间的内部联系,建立了从非线性ODE体系获取线性ODE体系的具体途径,并据此改写了COLEGN程序,简化了用户的输入,使之更易于使用,另外,还对边界条件含特征值的情况作了相应处理,拓宽了算法的适用范围。 An integrated algorithm of solving ODE eigenvalue problems was proposed before. A program code called COLEGN for solving this kind of problem was also developed based on this method, but the code requires the user to input both the equivalent nonlinear ODE system and the linear ODE system and hence is not easy to use. The essential relations between these two ODE systems are studied in this paper. It is found that the linear ODE system can be obtained completely from the nonlinear ODE system. The formulation to extract the linear ODE system is proposed in this paper and incorporated into COLEGN. The new COLEGN only needs the user to input the nonlinear ODE system and is easier to use. In addition, the case that the eigenvalue appears in the boundary conditions is also treated in this paper, which expands the algorithms applicability.
作者 叶康生 袁驷
出处 《工程力学》 EI CSCD 北大核心 2004年第3期31-35,77,共6页 Engineering Mechanics
基金 国家杰出青年科学基金 清华大学基础研究基金(JC2000001) 清华大学土木系基础基金资助项目
关键词 常微分方程 特征值 常微分方程求解器 自伴随 正交化 ordinary differential equation eigenvalue ordinary differential equation solver self-adjoint orthogonalization
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