计算物理 ›› 1993, Vol. 10 ›› Issue (3): 290-296.
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边少锋1, 吴晓平1, 刘权威2
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Bian Shaofeng1, Wu Xiaoping1, Liu Quanwei2
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摘要: 定义y/x作为新的变量z,将其与x作为一组新的变量(x,z)借以取代(x,y),结果表明这组新的变量(x,z)几乎可使位场与距离倒数1/r有关的奇异积分都非奇异。利用这组新的变量,本文给出了位场有关量的解析表示。本文还给了斜率变量使用前后的有关数值对比,结果表明在新变量形式下,数值积分收敛很快。
关键词: 奇异积分, 变量替换, 数值分析
Abstract: Definiting the slope y/x as a new variable z, the variable transformation from (x, y) to (x, z) is presented. It is found that such a set of new variable (x,z) almost makes the singular integrals dependent on the distance reciprocal r in potential fields become non-singular. By using the new variable, analytical expressions concerning common singular integrals in potential fields are derived as well. Numerical results show that the numerical integration con verges very fast with the method.
Key words: singular integral, variable transformation, numerical analysis
边少锋, 吴晓平, 刘权威. 位场奇异积分计算与斜率变量[J]. 计算物理, 1993, 10(3): 290-296.
Bian Shaofeng, Wu Xiaoping, Liu Quanwei. THE EVALUATION OF SINGULAR INTEGRALS IN, POTENTIAL FIELDS AND THE SLOPE VARIABLE[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 1993, 10(3): 290-296.
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