绝热非径向太阳振动的数值计算方法

本文采用改进后的平行Shooting方法，即连续正交归一化方法，通过增加系统的秩和把微分方程从线性变成非线性的方法，使得病态方程变成非病态方程，克服了平行Shooting方法（不连续正交归一化方法）的主要困难：一是选择径向网格点数目的问题，如果被检验振动模的径向节点数大或小，所需要的网格点数则多或少；二是在远离阈值的时候，尚未有合适的方法提高计算精度的问题．数值计算出了标准太阳模型的绝热非径向太阳振动的理论本征频率谱．从数值计算的结果发现改进后的平行Shooting方法比线性化的Henyey方法和平行Shooting方法收敛性更好且精度更高．其误差可以达到1％的精度．

The Numerical Method of Adiabatic Nonradial Solar Oscillations

This paper adopts modeficatory parallel shooting method, i.e. continuous orthonormalization method which changes the problem from a set of stiff ordinary differential equations to a set of non-stiff ordinary differential equations by increasing the order of the system and transforming the system from linear to nonlinear. As a result, the continuous orthonormalization method avoids those major dimculties with parallel shooting method, i.e., discrete orthonormaJization method. A major difficulty of this teclmique occtirs in the selection process of obtaining a mesh of radial points. if one is investigating modes with a laxge (small)number of radial nodes, then more (fewer) mesh points will be needed. Another difficulty is that beyond a certain threshold there is no cost-effective way to improve upon the computed eigenfrequencies. We calculate numerically some low-order n and low-degree l solar p-mode and g-mode eigenfrequencies for the standard solar model. Eigenfrequencies obtained with this method are computed more accurately and efficiently than with existing methods, and the dtherences between theory and observation agree at the 1% level.