Solusi Model Perubahan Garis Pantai dengan Metode Transformasi Elzaki

Abstract

. Pantai merupakan kawasan yang sering dimanfaatkan untuk berbagai kegiatan manusia, namun seringkali upaya pemanfaatan tersebut menyebabkan permasalahan pantai sehingga garis pantai berubah. Salah satu cara yang dapat digunakan untuk mengetahui perubahan garis pantai yaitu dengan membuat model matematika. Model perubahan garis pantai berbentuk persamaan diferensial parsial dapat diselesaikan secara analitik dengan menggunakan metode transformasi Elazki. Metode transformasi Elzaki merupakan salah satu bentuk transformasi integral yang diperoleh dari integral Fourier sehingga didapatkan transformasi Elzaki dan sifat-sifat dasarnya. Perubahan garis pantai pada penelitian ini dipengaruhi oleh adanya groin. Penyelesaian model perubahan garis pantai dengan metode transformasi Elzaki dilakukan dengan menerapkan transformasi Elzaki pada model perubahan garis pantai untuk memperoleh model perubahan garis pantai yang baru, kemudian menerapkan syarat batas, kemudian menerapkan invers transformasi Elzaki sehingga diperoleh solusi model perubahan garis pantai. Berdasarkan hasil penelitian, diperoleh bahwa terdapat kesamaan antara pola grafik yang dihasilkan dari solusi model perubahan garis pantai dengan metode transformasi Elzaki dan solusi model perubahan garis pantai dengan metode numerik.Kata Kunci: Perubahan garis pantai, Groin, Analitik, Transformasi Elzaki.The beach is a region that is often used for various human activities, however often these utilization efforts cause beach problems so that the shoreline changes. One way that can be used to determine changes in shoreline is to make a mathematical model. The shoreline change model shaped of partial differential equation can be solved analytically by using the Elzaki transform method. The Elzaki transform method is a form of integral transform obtained from the Fourier integral so that the Elzaki transform and its basic properties are obtained. Shoreline change in this research were affected by groyne. Solution of shoreline change model using Elzaki transform method is carried by applying the Elzaki transform to the shoreline change model to obtain a new shoreline change model, then applying the boundary value, then applying the inverse of Elzaki transform so obtained a solution shoreline change model. Based on the research result, it was found that there was a similiarity between the graphic patterns generated from the solution of shoreline change model using Elzaki transform method and the solution of shoreline change model using numerical method.Keywords: Shoreline change, Groyne, Analitic, Elzaki transform

Simulation on coastline change impacted by a groyne as shore protection

“…Equation ( 5) is the analytical solution for the coastline change model. Similar results were obtained using Elzaki transform [14]. While in [14], the groyne was positioned generally at a location x = w, where w can be any value, in this study a specific position is given which is at x = 0.…”

“…Similar results were obtained using Elzaki transform [14]. While in [14], the groyne was positioned generally at a location x = w, where w can be any value, in this study a specific position is given which is at x = 0. From equation (5), simulation on the coastline changes with respect to time can be observed.…”

“…Table 1 provides the mathematical symbols and their definitions that are used in this paper. Let the coastline changes be y(x, t), where x represents the spatial position and t represents time, the continuity equation reads [15]:…”

“…Equation (5) represent changes in coastline upstream and downstream of the groyne. In more detail, the derivation of this equation can be seen in [15].…”

“…This equation can be solved analytically so that the exact solution can be obtained. Wahyuni et al [14] implemented the Elzaki transformation in obtaining this solution. Another transform such as the Laplace transform can also be effectively used to solve this equation.…”