Balancing Terms and Polynomial Order in the Trial Equation with Correlation of Different Ansatz in HBM


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Authors

  • Divyanshu Dev Department of Mathematics and Scientific Computing, NIT Hamirpur, Himachal Pradesh, India
  • Sarita Pippal Department of Mathematics, Panjab University, Chandigarh, India
  • Saurabh Kapoor Department of Science and Mathematics, Regional Institute of Education (NCERT), Bhubaneswar, India

Keywords:

Trial Equation, Homogeneous Balance Method, Non-linear partial differential equations

Abstract

The Homogeneous Balance Method (HBM) is a reliable method solving Non-linear partial differential equations (NLPDEs). Within the framework of HBM, this manuscript investigates the degree of transformation that connects various Ansatz formulations with the polynomial order in the trial equation. Furthermore, a link is established between the trial equations under consideration and the Ansatz from different HBM-based approaches. It has been shown that different methods based on HBM are mirror images of each other. This equivalence can be achieved by appropriately adjusting the specific values of the balancing term and selecting the order of the Riccati equations.

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Published

30-12-2023

How to Cite

Divyanshu Dev, Sarita Pippal, & Saurabh Kapoor. (2023). Balancing Terms and Polynomial Order in the Trial Equation with Correlation of Different Ansatz in HBM. International Journal of Mathematics And Its Applications, 11(4), 197–206. Retrieved from https://ijmaa.in/index.php/ijmaa/article/view/1590

Issue

Vol. 11 No. 4 (2023)

Section

Research Article

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