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In this letter, the leapfrog scheme-based precise integration time domain (L-PITD) method is proposed to decrease the memory requirements of the precise integration time domain (PITD) method. In the L-PITD method, the electromagnetic field components are divided into two groups so as to split up a 3-D problem to a set of 2-D problems. And then a leapfrog scheme is proposed to solve these 2-D problems by using the precise integration technique. The numerical results confirm that the L-PITD method not only is stable with the time step size much larger than the Courant-Friedrich-Levy limit of the finite difference time domain method, but also has significant advantages over the PITD method with respect to the execution time and the memory requirements.