Skip to main content

Solution of Gas Dynamic and Wave Equations with VIM

  • Conference paper
  • First Online:
Advances in Fluid Dynamics

Part of the book series: Lecture Notes in Mechanical Engineering ((LNME))

Abstract

In the present research paper, we will solve homogeneous and non-homogeneous gas dynamics equation, KdV, K (2, 2) equations and wave equation with different boundary conditions. In the current research paper, to arbitrate solutions for KdV, the K (2, 2) and the wave equation reliable iteration approach is taken into consideration. We apply VIM to solve all the equations. The study highlights the efficiency of the approach and its confidence on the Lagrange multiplier. This work completes the coordination of KdV condition by the guide of any other strategy. This prompts the unpredictable answers for the condition of homogeneous and non-homogeneous gas dynamics equation, KdV and wave equations.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 259.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 329.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Salih, Burger’s equation. Indian Institute of Space Science and Technology, Thiruvananthapuram—18 Feb 2016

    Google Scholar 

  2. Grimshaw R (2008) Kortwege-de varies equation. Loughborough University, UK, 11 Jan 2008

    Google Scholar 

  3. Hamid P. Application of extended Tanh method to generalized burgers-type equations. Department of Mathematical Sciences, Safahan College, Isfahan 81747–43196, Iran

    Google Scholar 

  4. Singh V, Rani M, Bhatti HS (2017) Analytical solution of (1+n) dimensional nonlinear Burgers’ equation using variational iteration method. In: Proceedings of the World Congress on Engineering 2017, vol I WCE 2017, 5–7 July 2017, London, U.K

    Google Scholar 

  5. He JH (1998) A variational iteration approach to nonlinear problems and its applications. Mech Appl 30–31

    Google Scholar 

  6. He JH (2004) Variational principles for some nonlinear PDE with variable coefficients. Chaos, Solitons Fractals 19:847–851

    Article  MathSciNet  Google Scholar 

  7. He JH (2000) Variational iteration method for autonomous ordinary differential systems. Appl Math Comput 114:115–123

    MathSciNet  MATH  Google Scholar 

  8. Jawad AJM, Petkovic MD, Biswas A (2010) Soliton solutions of Burgers equations and perturbed Burgers equation. Appl Math Comput 216:3370–3377

    Google Scholar 

  9. Wazwaz M (2007) The variational iteration method for rational solutions for KdV, K(2,2), Burgers, and cubic Boussinesq equations. J Comput Appl Math 207(1):18–23

    Article  MathSciNet  Google Scholar 

  10. He JH (2006) Some asymptotic methods for strongly nonlinearly equations. Int J Modern Math 20(10):1141–1199

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Nahid Fatima .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2021 Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Fatima, N. (2021). Solution of Gas Dynamic and Wave Equations with VIM. In: Rushi Kumar, B., Sivaraj, R., Prakash, J. (eds) Advances in Fluid Dynamics. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-15-4308-1_6

Download citation

  • DOI: https://doi.org/10.1007/978-981-15-4308-1_6

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-15-4307-4

  • Online ISBN: 978-981-15-4308-1

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics