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含两种介质球壳内电势的半球区间积分解法

Keywords: 勒让德多项式, 正交性, 无穷级数, 收敛性??

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Abstract:

在半球形介质以及球形界面一侧含有两种不同介质的静电问题中,由于勒让德多项式在这类区间上的非正交性,应用半球区间积分方法得到的电势一般是以无穷级数的形式给出的,它的收敛性通常由于实际问题的复杂性而是假定的.为研究此方法所得解的收敛性,应用此方法求解球壳内含两种不同介质的静电问题,并将所得电势的级数解与它的精确解相比较,结果二者完全一致,表明该方法对求解此类问题的有效性,同时也给出球壳静电问题一个全新的解法.

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