The formulations of the shallow water equations are deduced from the cube sphere coordinate in the paper.Using the modified differential quadrature(MDQ) special difference scheme and fourth order Runge-Kutta scheme to solve the shallow water equations

the vector velocity expressions of six regions in the linear advection of a cosine bell case are given from the cube sphere coordinate.The paper computes the three cases of the linear advection of a cosine bell.An explicit hyperdiffusion term (-

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) was used to free the numerical solutions from the noise introduced at the internal boundaries by the interpolation procedure.The method features the following advantages: ① fully explicit;② fourth order of accuracy in time;③ high order of accuracy in space by changing only one parameter;④ robust in proceeding numerical problem.