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Abnormity of super low frequency (SLF) and extremely low frequency (ELF) electromagnetic radiation on the satellite has been discovered before the earthquakes occur by the earthquake prediction researchers. In order to estimate the effects on the electromagnetic radiation in the lower ionosphere associated with the seismic activity, SLF/ELF waves radiated from a possible seismic current source modeled as an underground horizontal electric dipole (HED), are precisely computed by using a speeding numerical convergence algorithm. Its main feature and its originality of this algorithm are that the appropriate identical terms are subtracted and added to the original exact series. The subtraction accelerates significantly its numerical convergence. The added terms sum to simple closed-form expressions. It needs 700 series items and takes 10 min by the calculation directly sum of the series algorithm, while it only needs 100 series items and takes 0.3 min by the speeding numerical convergence algorithm. So the series items decreases and the speed is also greatly improved. The field intensity during night is less than that during day, and its change is small. Because the absorption loss of the ionosphere is very big, the field intensity in the lower ionosphere greatly decreases along the altitude.