Method for Determining Weighting Coefficients in Weighted Taylor Series Applied to Water Wave Modeling

The Weighted Taylor series is an adaptation of the conventional Taylor series truncated to the first order, wherein high-order differential terms are replaced by introducing weighting coefficients to the initial terms. This study presents a novel approach for computing these weighting coefficients specifically designed for water wave modeling. Subsequently, the derived weighted Taylor series is employed to formulate both weighted continuity and the weighted Laplace equation. The weighted Laplace equation facilitates the formulation of the velocity potential equation, leading to the development of wave transformation equations encompassing important phenomena such as shoaling, breaking, and refraction-diffraction. Additionally, the formulation of the weighted Euler momentum conservation equation is introduced to determine the wave number in deep water. By scrutinizing the outcomes of dispersion equations, as well as analyzing shoaling-breaking and refraction-diffraction scenarios, optimal values for the weighting coefficients are identified..