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By the separation of singularity, a special Fourier series solution of the boundary valueproblem for plane is obtained, which can satisfy all boundary conditions and converges rapidly. It isproved that the solution is equal to the result of separation of variables. As a result, the non-linearcharacteristic equations resulting from the method of separation of variables are transformed into poly-nomial equations that can provide a foundation for approximate computation and asymptotic analysis.
By the separation of singularity, a special Fourier series solution of the boundary valueproblem for plane is obtained, which can satisfy all boundary conditions and converges rapidly. It isproved that the solution is equal to the result of separation of variables. non-linearcharacteristic equations resulting from the method of separation of variables are transformed into poly-nomial equations that can provide a foundation for approximate computation and asymptotic analysis.