Solitary Wave Solutions for Forced Nonlinear Korteweg-de Vries Equation by Using Approximate Analytical Method

Authors

  • Che Haziqah Che Hussin Preparatory Centre for Science and Technology, Universiti Malaysia Sabah, Jalan UMS, 88400 Kota Kinabalu, Sabah, Malaysia
  • Arif Mandangan Faculty of Science and Natural Resources, Universiti Malaysia Sabah, Jalan UMS, 88400 Kota Kinabalu, Sabah, Malaysia
  • Amirah Azmi School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM Penang, Malaysia
  • Adem Kilicman Institute for Mathematical Research, Universiti Putra Malaysia, 43400 UPM Selangor, Malaysia

DOI:

https://doi.org/10.37934/arfmts.99.2.197206

Keywords:

Adomian polynomials, Multistep approach, modified Reduced Differential Transform Method, forced NKdV equations, shallow water waves, tsunami

Abstract

The Multistep Modified Reduced Differential Transform Method (MMRDTM) is proposed in this paper. It is implemented to solve the forced nonlinear Korteweg-de Vries (fnKdV) equations. There are several advantages of the proposed method. Using the suggested approach, a high-speed converging series can be approximated analytically. Furthermore, the number of calculated terms is reduced significantly. The nonlinear term in fnKdV equations is substituted with corresponding Adomian polynomials before applying the multi-step technique. As a result, we provided simpler and more effective ways to solve fnKdV equations. On top of that, the solutions can be approximated more accurately over a longer period of time. To show the MMRDTM's capability and accuracy, we consider several of the fnKdV examples to illustrate the proposed method’s potential in analytical approximation. Then, the features of the solutions are represented in tabular and graphical forms. In conclusion, the proposed method delivers highly accurate and precise solutions for these types of equations.

Author Biographies

Che Haziqah Che Hussin, Preparatory Centre for Science and Technology, Universiti Malaysia Sabah, Jalan UMS, 88400 Kota Kinabalu, Sabah, Malaysia

haziqah@ums.edu.my

Arif Mandangan, Faculty of Science and Natural Resources, Universiti Malaysia Sabah, Jalan UMS, 88400 Kota Kinabalu, Sabah, Malaysia

arifman@ums.edu.my

Amirah Azmi, School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM Penang, Malaysia

amirahazmi@usm.my

Adem Kilicman, Institute for Mathematical Research, Universiti Putra Malaysia, 43400 UPM Selangor, Malaysia

akilic@upm.edu.my

Downloads

Published

2022-09-22

How to Cite

Che Haziqah Che Hussin, Arif Mandangan, Amirah Azmi, & Adem Kilicman. (2022). Solitary Wave Solutions for Forced Nonlinear Korteweg-de Vries Equation by Using Approximate Analytical Method. Journal of Advanced Research in Fluid Mechanics and Thermal Sciences, 99(2), 197–206. https://doi.org/10.37934/arfmts.99.2.197206

Issue

Section

Articles