ANALYTICAL APPROXIMATE SOLUTION FOR THE FORCED KORTEWEG-DE VRIES (FKDV) ON CRITICAL FLOW OVER A HOLE USING HOMOTOPY ANALYSIS METHOD

Authors

  • Vincent Daniel David UTM Centre for Industrial and Applied Mathematics, Ibnu Sina Institute for Scientific & Industrial Research, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia
  • Zainal Abdul Aziz UTM Centre for Industrial and Applied Mathematics, Ibnu Sina Institute for Scientific & Industrial Research, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia
  • Faisal Salah Department of Mathematics, Faculty of Science, University of Kordofan, North Kordofan State, 51111 El-Obeid, Sudan

DOI:

https://doi.org/10.11113/jt.v78.7823

Keywords:

fKdV equation, homotopy analysis method, approximate analytical solution, holed bottom topography

Abstract

Free surface flows in a two-dimensional channel past over a hole is studied using shallow water forced Korteweg-de Vries (fKdV) equation. The forcing term of fKdV equation represents the hole shaped bottom topography. Froude number (Fr), which represents the ratio of flow speed to the wave speed, will also be used in solving fKdV equation. The fKdV equation is solved using Homotopy Analysis Method (HAM). HAM is an approximate analytical technique used to obtain series of solutions for the nonlinear problems where HAM has an auxiliary parameter coto adjust and control the convergence region of the series solution. Solitary wave solutions are obtained from the series of solutions of HAM and wave flows are observed at particular time. The HAM solution shows the hole shaped bottom topography plays an important role in determining the evolution of solitary waves. 

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Published

2016-03-09

How to Cite

ANALYTICAL APPROXIMATE SOLUTION FOR THE FORCED KORTEWEG-DE VRIES (FKDV) ON CRITICAL FLOW OVER A HOLE USING HOMOTOPY ANALYSIS METHOD. (2016). Jurnal Teknologi (Sciences & Engineering), 78(3-2). https://doi.org/10.11113/jt.v78.7823