In this study, the Taylor series is formulated with a weighted coefficient to time step and spatial interval. With the weighted Taylor series, the weighted total acceleration is formulated on Euler's momentum equation and the Kinematic Free Surface Boundary Condition (KFSBC).The final part is the development of a time series water wave model using the weighted momentum Euler equation and the weighted KFSBC. I.

Analytical solution of Laplace equation using variable separation method, consists of two velocity potentials. However, only one component has been used. This research used both velocity potential equation components. With the potential equation, water wave surface equation and the related wave constants were formulated using kinematic free surface boundary condition and surface momentum equation. The characteristic of water wave surface that was produced was observed, both in deep water and shallow water.

In this research, total acceleration equation is formulated where there is time scale coefficient at its time differential term. The formulation was done based on Courant Number equation and by using Taylor series. Then this total acceleration is applied to kinematic free surface boundary condition and Euler momentum equations. Potential velocity and water surface equations of linear water wave theory as well as wave number conservation equation were substituted to momentum and kinematic free surface boundary condition equations produced dispersion equation with wave amplitude as its variable and which fits with wave number conservation equation. Wave number conservation equation is an equation that regulates changes in wavelength as a result of water depth changes. This equation was extracted from potential velocity equation.

This paper presents the time-step and grid-size calculation methods for solving time series wave differential equations using the Finite Difference Method.The methods are formulated using the Taylor series, assuming that at a very small time-step and grid-size, the number of terms in the Taylor series starting with 2nd order with the highest order is much smaller than the order 1. I.

Continuity equation for wave modeling is still being developed. There are quite a lot of versions of this equation. This research formulates continuity equation in a simple form to simplify its numerical and analytical solution. The formulation of the continuity equation is done by performing mass conservation law in a water column with free surface and by performing weighted total acceleration. Then, the continuity equation is performed along with the surface momentum equation and completed numerically to modeling one-dimensional wave dynamism. The equation is capable of modeling shoalingand breaking.