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In this paper, a compact finite difference method is presented for solving the initial boundary value problems for the improved Boussinesq equation with damping terms. The fourth-order equation can be transformed into a first-order ordinary differential system, and then, the classical Padé approximation is used to discretize spatial derivative in the nonlinear partial differential equations. The resulting coefficient matrix for the semi-discrete scheme is tri-diagonal and can be solveddoi:10.4208/jcm.1603-m2014-0193 fatcat:ad2fvvhjkffnvfnbyxcuyhbglm