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

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.

References

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Published

2024-02-15

How to Cite

Haizar, M. R., Rizki, M., Robbaniyyah, N. A., Syechah, B. N., Salwa, S., & Awalushaumi, L. (2024). Numerical Solution of the Korteweg-De Vries Equation Using Finite Difference Method. EIGEN MATHEMATICS JOURNAL, 7(1), 1–7. https://doi.org/10.29303/emj.v7i1.190

Issue

Vol. 7 No. 1 (2024): June

Section

Articles

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