Numerical Solution of the Korteweg-De Vries Equation Using Finite Difference Method

Maulana Rifky Haizar; Miptahul Rizki; Nuzla Af'idatur Robbaniyyah; Bulqis Nebulla Syechah; Salwa Salwa; Lailia Awalushaumi

doi:10.29303/emj.v7i1.190

Authors

Maulana Rifky Haizar Universitas Mataram
Miptahul Rizki Universitas Mataram
Nuzla Af'idatur Robbaniyyah Universitas Mataram
Bulqis Nebulla Syechah Universitas Mataram
Salwa Salwa Universitas Mataram
Lailia Awalushaumi Universitas Mataram

DOI:

https://doi.org/10.29303/emj.v7i1.190

Keywords:

Equation KdV, Soliton, Finite difference method, Crank-nicolson scheme

Abstract

The Korteweg-de Vries (KdV) equation is a nonlinear partial differential equation that has a key role in wave physics and many other disciplines. In this article, we develop numerical solutions of the KdV equation using the finite difference method with the Crank-Nicolson scheme. We explain the basic theory behind the KdV equation and the finite difference method, and outline the implementation of the Crank-Nicolson scheme in this context. We also give an overview of the space and time discretization and initial conditions used in the simulation. The results of these simulations are presented through graphical visualizations, which allow us to understand how the KdV solution evolves over time. Through analysis of the results, we explore the behavior of the solutions and perform comparisons with exact solutions in certain cases. Our conclusion summarizes our findings and discusses the advantages and limitations of the method used. We also provide suggestions for future research in this area.

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