THERMAL SCIENCE

International Scientific Journal

Thermal Science - Online First

Authors of this Paper

External Links

online first only

Haar wavelets scheme for solving the unsteady gas flow in four-dimensional

ABSTRACT
The system of unsteady gas flow of four-dimensions is solved successfully by alter the possibility of an algorithm based on collocation points and four-dimensional Haar wavelet method (HWM). Empirical rates of convergence of the HWM are calculated which agree with theoretical results. To exhibit the efficiency of the strategy, the numerical solutions which are acquired utilizing the recommended strategy demonstrate that numerical solutions are in a decent fortuitous event with the exact solutions.
KEYWORDS
PAPER SUBMITTED: 2019-01-01
PAPER REVISED: 2019-06-15
PAPER ACCEPTED: 2019-06-22
PUBLISHED ONLINE: 2019-07-06
DOI REFERENCE: https://doi.org/10.2298/TSCI190101292A
REFERENCES
  1. Mahmood Farzaneh-Gord, Hamid Reza Rahbari, Unsteady natural gas flow within pipeline network, an analytical approach, Journal of Natural Gas Science and Engineering, 28, (2016), 397-409.
  2. A.S. Rashed, Analysis of (3+1)-dimensional unsteady gas flow using optimal system of lie symmetries, Mathematics and Computers in Simulation, Mathematics and Computers in Simulation, 156, (2019), 327-346.
  3. F. Oliveri, M.P. Speciale, Exact solutions to the unsteady equations of perfect gases through Lie group analysis and substitution principles, Int. J. Non-Linear Mech. 37 (2) (2002) 257-274.
  4. Leonid Plotnikov, Alexandr Nevolin and Dmitrij Nikolaev, The flows structure in unsteady gas flow in pipes with different cross-sections, EPJ Web of Conferences 159, 00035 (2017).
  5. V. A. Titarev1and E. M. Shakhov, Unsteady Rarefied Gas Flow with Shock Wave in a Channel, Fluid Dynamics, 53, (2018), 143-151.
  6. T. Raja Sekhar, V.D. Sharma, Similarity solutions for three dimensional Euler equations using Lie group analysis, Appl. Math. Comput.196 (1) (2008) 147-157.
  7. S. Arbabi, A. Nazari, M.T. Darvishi, "A two dimensional Haar wavelets method for solving system of PDEs" Applied Mathematics and Computation,292, (2017), 33-46.
  8. A. Arnold, "Numerically absorbing boundary conditions for quantum evolution equations", VLSI Design, 6, (1998) 313-319.
  9. I. Celik, "Haar wavelet method for solving generalized Burger Huxley equation", Arab Journal of Mathematical Sciences, 18, (2012) 25-37.
  10. I. Singh, S. Kumar, "Haar wavelet and Adomain decomposition method for solving third order partial differential equations arising in impulsive motion of a flat plate", International Journal of Mathematical Modeling and Computation, 6, 2, (2016) 175-188.
  11. I. Singh, S. Kumar, "Wavelet methods for solving three-dimensional partial differential equations", Mathematical Sciences, 11, 2, (2017)145-154.
  12. Siraj-ul-Islam, I. Aziz, A.S. Al-Fhaid and A. Shah, "A numerical assessment of parabolic partial differential equations using Haar and Legendre wavelets", Applied Mathematical Modelling,37, (2013), 9455-9481.
  13. A. Kaushik, A. Kumar, "Numerical study of steady one-dimensional Incompressible flow through a nozzle using simple algorithm", International Journal of Scientific Research in Mathematical and Statistical Sciences, 3, 5, (2016), 1-7.
  14. J. Biazar, M. Eslami, A new homotopy perturbation method for solving systems of partial differential equations, Comput. Math. Appl. 62 (2011), 225-234.
  15. M. Matinfar, M. Saeidy, B. Gharahsuflu, A new homotopy analysis method for finding the exact solution of systems of partial differential equations, Selçuk J. Appl. Math. 13 (2012) 41-56.
  16. K. Yildirim, A solution method for solving systems of nonlinear PDEs, World Appl. Sci. J. 18 (2012) 1527-1532.
  17. Y. Li, W. Zhao, Haar wavelet operational matrix of fractional order integration and its applications in solving the fractional order differential equations,Appl. Math.Comput. 216 (2010) 2276-2285.
  18. S.S. Ray, On Haar wavelet operational matrix of general order and its application for the numerical solution of fractional Bagley-Torvik equation, Appl.Math. Comput. 218 (2012) 5239-5248.
  19. S.S. Ray, A. Patra, Haar wavelet operational methods for the numerical solutions of fractional order nonlinear oscillatory van der Pol system, Appl.Math. Comput. 220 (2013) 659-667.
  20. A. Patra, S.S. Ray, Two-dimensional Haar wavelet collocation method for the solution of stationary neutron transport equation in a homogeneous isotropic medium, Ann. Nucl. Energy 70 (2014) 30-35.
  21. S.S. Ray, A.K. Gupta, A two-dimensional Haar wavelet approach for the numerical simulations of time and space fractional Fokker-Planck equations in modelling of anomalous diffusion systems, J. Math. Chem. 52 (2014) 2277-2293.
  22. S.S. Ray, A.K. Gupta, An approach with Haar wavelet collocation method for numerical simulations of modified KdV and modified Burgers equations, Comput. Model. Eng. Sci. 103 (2014) 315-341.
  23. K. Yildirim, A solution method for solving systems of nonlinear PDEs, World Appl. Sci. J. 18 (2012) 1527-1532.
  24. S. Arbabi, A. Nazari, M.T. Darvishi, A semi-analytical solution of Hunter-Saxton equation, `Optik 127 (2016) 5255-5258.
  25. T. Raja Sekhar, V.D. Sharma, Similarity solutions for three dimensional Euler equations using Lie group analysis, Appl. Math. Comput.196 (1) (2008) 147-157.
  26. R.E. Bellman, R.E. Kalaba, Quasilinearization and Nonlinear Boundary-Value Problems, American Elsevier Pub. Co., (1965).
  27. J. Biazar, M. Eslami, A new homotopy perturbation method for solving systems of partial differential equations, Comput. Math. Appl. 62 (2011) 225-234.
  28. M. Mtinfar, M. Saeidy, B. Gharahsuflu, A new homotopy analysis method for finding the exact solution of systems of partial differential equations, Selçuk J. Appl. Math. 13 (2012) 41-56.