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Abstract
In tsunami research, dispersive wave theory is used to numerically simulate transoceanic and near-field propagation by soliton fission. Many numerical schemes have been proposed to solve the dispersive wave effect, but there has been no reliable criterion for selecting an adequate scheme. To address this, we derive exact numerical stability solutions to the linear finite difference equations of dispersive wave theory by using several numerical methods. Characteristics of the truncation error and the numerical stability of the methods are discussed, and the leap-frog implicit scheme appears to be applicable to practical problems due to its superior stability. A new numerical model that uses an implicit scheme is proposed based on the above results. The dispersive term in the equation of motion is solved by a Poisson-type differential equation and the model can be extended to the nonlinear physics. This model is validated by being compared to the conventional models, and it is applied to a Tonankai-Nankai tsunami as an example of a practical problem. The model shows excellent agreement with both the linear analytical solution and the laboratory experiments. Furthermore, the solutions to this model require less computing time than those of the conventional models.