# Discrete fractional numerical analysis on the shallow water wave theory

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## Keywords:

shallow waves, approximations, waves distribution, coastal engineering, mathematical techniques, errors## Abstract

In order to address the wave height distribution in any region, from deep ocean to shallow water,

coastal engineering, electromagnetic wave propagation and scattering, and acoustics, this study introduces

numerical methods to tackle a variety of problems in wave theory. At that point, numerical analysis and

techniques become useful in assisting us in obtaining the most accurate approximation possible for our

barrier.

The core formulas of our numerical analysis technique are the linearized wave equations with unknown

functions only at the water surface, like the particle velocity components and the elevation of the water

surface, which are derived from the Eulerian equations of motion and continuity assuming small amplitude

in constant water depth.

We quantify the accuracy of discretization solution techniques such as finite difference or finite elements

schemes in powers of a discretization step size h. The Nemerov system is useful. A method with p > 2 is

typically referred to as a higher order method, and one with error O (h

p

) is said to be of order p.

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*International Journal of Advanced Natural Sciences and Engineering Researches*,

*8*(5), 129–139. Retrieved from https://as-proceeding.com/index.php/ijanser/article/view/1894