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We compare recent global MHD simulation models of the terrestrial magnetosphere based on different numerical schemes. The schemes include the finite-difference method based on the modified leapfrog (MLF) scheme, and the semi-Lagrangian scheme based on the constrained interpolation profile (CIP) algorithm. With the two models, we examined the simulation under a northward interplanetary magnetic field (IMF) condition. As a result, we found out that the two simulation models give consistent results on the magnetopause locations at the subsolar point and the terminator, and the overall structures of the cusp in the meridian plane. However, discrepancies are also found in the location and jump conditions of the bow shock. The MLF model showed higher thermal pressure value and weaker magnetic field strength in the downstream than those in the CIP model. The difference in the jump condition across the shock is also reflected in the difference in the length of the magnetotail in the two models. The magnetotail is shorter in the CIP model than that in the MLF model. We conclude that further comparative studies with finite-volume methods are necessary to verify the solution of the bow shock formation and the location of the last closed field line under northward IMF conditions.