三维时域波动函数的一种数值处理方法

A Numerical Calculating Method for the 3-D Time Dependent Wave Function

把满足线性自由面边界条件的三维时域波动函数（三维时域格林函数的波动项部分）及其有关导数的数值计算问题分为小时间和大时间的计算区域来进行计算，在小时间的情况下把上述有关函数展开为台劳级数并归结为有关的勒让德多项式的计算。在大时间的情况下，先把上述有关函数化为包含有合流超几何函数的积分表达形式，然后对合流超几何函数进行渐近展开，利用最陡下降法原理处理有关积分问题。利用本方法对上述函数进行了实用计算，证明了该数值处理方法的有效性。

A 3-D time dependent wave function,or a wave term of 3-D time dependent Green'sfunction,which satsfies the linear free surface boundary conditions, and its reled deriva-tives are separtely calculated in short time interval and long time interval regions。For shorttime interval regions,the functions are expanded into Taylor series and calculated by Legen-dre polynomial numerically.for long time interval ones,the wave function and is relatedderivatives are expressed first innterms of integration containing appropriate confluent hyper-geometric functions. Then,by asymptotic expansion,the integrations are handled with theSteepest Descent Method.Actual calculation results show the usefulness of the method pro-posed。