In this paper a finite difference scheme for the one-dimensional double dispersion equation is constructed and studied. The scheme is based on the representation of this equation as a generalized Hamiltonian system. After applying the partitioned Runge-Kutta method with 3-stage Lobatto IIIA and IIIB coefficients, we get a discrete finite difference scheme with approximation error O(h~2 + τ~4). This scheme is symplectic, i.e. it preserves the symplectic structure of the solution on the discrete level. Numerical experiments are provided for quadratic nonlinearity. Two problems are considered: propagation of a single solitary wave and interaction of two waves traveling toward each other. The numerical results show the convergence of the discrete solution to the exact one with O(h~2 + τ~4) error.
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