| Summary: | 碩士 === 國立中山大學 === 應用數學系 === 87 === For the benchmark of singularity problems, Motz's problem, two
most accurate numerical methods are provided: (1) The conformal
transformation method (CTM) for the leading coefficients in the solution expansions. (2) The boundary approximation methods (BAM) for the entire solutions.
In this paper, new analysis on truncation and rounding errors is
made to guarantee very high accuracy of singular coefficients of the Motz solutions.
Most importantly, we provide the following most accurate leading coefficients of the Motz solutions ever published so far, which may be used to test new algorithms for singularity
problems in the 21th century.
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