Two Reliable Computational Techniques for Solving the MRLW Equation

Kamel Al-Khaled*, Haneen Jafer

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


In this paper, a numerical solution of the modified regularized long wave (MRLW) equation is obtained using the Sinc-collocation method. This approach approximates the space dimension of the solution with a cardinal expansion of Sinc functions. First, discretizing the time derivative of the MRLW equation by a classic finite difference formula, while the space derivatives are approximated by a (Formula presented.) weighted scheme. For comparison purposes, we also find a soliton solution using the Adomian decomposition method (ADM). The Sinc-collocation method was were found to be more accurate and efficient than the ADM schemes. Furthermore, we show that the number of solitons generated can be approximated using the Maxwellian initial condition. The proposed methods’ results, analytical solutions, and numerical methods are compared. Finally, a variety of graphical representations for the obtained solutions makes the dynamics of the MRLW equation visible and provides the mathematical foundation for physical and engineering applications.

Original languageEnglish
Article number174
Issue number2
Publication statusPublished - Feb 2023


  • Adomian decomposition method
  • MRLW equation
  • sinc-collocation method
  • soliton solutions

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Mathematical Physics
  • Logic
  • Geometry and Topology

Cite this