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April 16, 2026CAUCHY Jurnal Matematika Murni dan AplikasiOpen Access

Higher-Order Numerical Solution of the KdV-BBM Equation: A Comparative Analysis of Temporal Integration Schemes in the Method of Lines Framework

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Authors

DADita ArdianaUniversity of BrawijayaUHUmmu HabibahTTTrisilowati TrisilowatiUniversity of Brawijaya

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Overview

Comparative analysis demonstrates that iRK-5 improves accuracy in numerical simulations of solitary waves, suggesting better performance for complex wave phenomena.

Key Points

  • The aim is to compare three temporal integration schemes in the MOL framework for simulating the KdV-BBM equation.
  • Transformed the KdV-BBM equation into a system of ordinary differential equations via spatial discretization.
  • Evaluated the performance of the first-order Euler method, fourth-order Runge-Kutta (RK-4), and fifth-order iRK-5.
  • Performed quantitative analysis using Mean Absolute Error (MAE) for different time steps.
  • The iRK-5 method achieved a maximum accuracy level of 4.55e-6 at a coarser time step of t = 0.1.
  • RK-4 required a finer time step of t = 0.05 to reach similar precision.
  • Both high-order methods reached a spatial error floor, with diminished effect from further temporal refinement.

Cite This Study

Ardiana et al. (2026) studied this question.

synapsesocial.com/papers/69e07cfa2f7e8953b7cbdfd7https://doi.org/10.18860/cauchy.v11i1.41525
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