【摘要】 证明了，如果某微分方程的基本解中含有对数函数，那么目前习用的边界积分方程的解可能不是原微分方程边值问题的解。如果把此类边界积分方程用边界元法离散化求近似解，那么这些近似解将依赖于用作无量纲化的长度标尺。其他情况相同，仅仅因为选取不同的长度标尺，就可使这些近似解彼此相差甚远。本文指出，文［２］开创的新一类边界积分方程与原微分方程边值问题对等，并且数值结果稳定，在工程上可放心使用。更多还原

【Abstract】 It is proved that the solutions of customary boundary integral equation,may not be those of theoriginal boundary value problems of differential equations when the fundamental solutions of the differentialequations contain logarithmic functions.When these houndary integral equations are discretized by boundaryelement method,the resulted approximate solutions depend on the length scale for nondimensionizing.Theapproximate solutions may be quite different for different length scales. It is pointed out that the new type ofboundary integral equations initiated in reference[2] is equivalent to the original boundary value problems.Moreover, the approximate numerical solutions obtained by the boundary element method are stable so that theyare reliable for practical uses.更多还原