A mixed approximate method to simulate generalized Hirota-Satsuma coupled KdV equations

초록

A mixed approximate method is proposed to simulate the generalized Hirota-Satsuma coupled Korteweg-de Vries equations. The equations are represented as linear dispersive equations for the material time derivative along the trajectory of physical particle movements described by the nonlinear Cauchy problem in the Lagrangian viewpoint. The proposed method employs the finite difference method and backward differentiation formula to solve the linear dispersive equations. To solve the nonlinear Cauchy problem, an error correction technique is applied. Moreover, the fifth-order weighted essentially non-oscillatory scheme interpolates solutions of non-grid points to control unnecessary oscillation due to the dispersion of the solution. From numerical experiments, we demonstrate the accuracy and efficiency of the proposed method. The proposed method numerically has the qth-order temporal and 4th-order spatial accuracies in the sense of the error norms L-infinity and L-2. Consequently, the errors obtained using the proposed method are more accurate even with a larger time step size than those of the compared methods.

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