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<p>The Benjamin–Bona–Mahony equation (BBME) is a nonlinear model employed in various scientific and engineering disciplines. It is particularly useful in oceanography for studying the dynamics of shallow water waves in density-stratified seas, especially when internal gravity waves are present. However, finding analytical solutions for highly nonlinear physical models like BBME is a challenging task. This paper focuses on deriving numerical solutions for BBME using the differential quadrature method (DQM). The DQM employs grid points based on shifted legendre polynomials (SLP) and generalized Laguerre polynomials (GLP) to solve BBME. The solutions obtained through DQM are compared with those derived from other methods. Finally, a comparison with the actual solution is carried out, revealing favorable agreement in the good results.</p>

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Numerical solutions of the Benjamin–Bona–Mahony equation using the differential quadrature method with shifted legendre and generalized Laguerre polynomials

  • 期刊论文

  • 发表日期：

    2025年1月18日

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  • Rambabu Vana,
  • Perumandla Karunaka

摘要

The Benjamin–Bona–Mahony equation (BBME) is a nonlinear model employed in various scientific and engineering disciplines. It is particularly useful in oceanography for studying the dynamics of shallow water waves in density-stratified seas, especially when internal gravity waves are present. However, finding analytical solutions for highly nonlinear physical models like BBME is a challenging task. This paper focuses on deriving numerical solutions for BBME using the differential quadrature method (DQM). The DQM employs grid points based on shifted legendre polynomials (SLP) and generalized Laguerre polynomials (GLP) to solve BBME. The solutions obtained through DQM are compared with those derived from other methods. Finally, a comparison with the actual solution is carried out, revealing favorable agreement in the good results.