大气潮汐全日振荡模本征值本征函数问题的数值计算

本文用有限阶截断矩阵和抛物线叠代近似求根法数值求解了大气潮汐全日振荡模的本征值一本征函数问题,求得了20×20阶截断本征值和本征向量。计算结果表明本征值的虚部比实部小若干量级,从而由计算实验证实了大气潮汐本征值问题有限阶截断矩阵的近似厄密特性。文中还叙述了变矩阵阶次以确定计算收敛性的实验结果,并与前人的结果进行了对比分析。

NUMERICAL CALCULATIONS OF THE EIGENVALUE- EIGENFUNCTION PROBLEM FOR THE DIURNAL MODE OF THE ATMOSPHERIC TIDE

Using an approach of truncated matrices and Muller's method （parabolic iteration）,the author has calculated numerically a set of eigenvalue-eigenfunctions for the diurnal mode of the atmospheric tide. Table 5 in the text gives the 20 X 20 order truncated eigenvalues for the symmetrical diurnal mode of the atmospheric tide derived by us.. It can be seen from these calculations that the imaginary part of the eigenvalue are several orders of magnitude less than the real part,therefore the approximate Hermi-tian nature of the matrices truncated in finite order is thus confirmed. Also a calcula-tion experiment to ascertain the convergence characteristics of the truncated matrix and a comparison between our values and those obtained by S. Kato are briefly discus-sed in this paper.