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Tytuł artykułu

An approximate analytic solution for isentropic flow by an inviscid gas model

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Języki publikacji
EN
Abstrakty
EN
The aim of the present analysis is to apply the modified decomposition method (MDM) for the solution of isentropic flow of an inviscid gas model (IFIG). The modification form based on a new formula of Adomian’s polynomials (APs). The new approach provides the solution in the form of a rapidly convergent series with easily computable components and not at grid points. The proof of convergence of MDM applied to such systems is introduced with a bound of the error. Using suitable initial values, the solution of the system has been calculated and represented graphically. An analytic continuous solution with high accuracy was obtained.
Rocznik
Strony
203--212
Opis fizyczny
Bibliogr. 19 poz., rys. kolor.
Twórcy
  • Department of Mathematics and Statistics Mutah University Mutah P. O. Box 7, Al Karak, Jordan
Bibliografia
  • 1. G. Adomian, A review of the decomposition method in applied mathematics, J. Math. Anal. Appl., 135,501–544, 1988.
  • 2. G. Adomian, Solving frontier problems of physics: the decomposition method, Kluwer Academic, Dordrecht, 1994.
  • 3. K. Al-khaled, M. N. Anwar, Numerical comparison of methods for solving second-order ordinary initial value problems, Appl. Math. Model., 31, 292-301, 2007.
  • 4. A. Aminateis, S. Hosseini, The comparison of the stability of Adomian decomposition method with numerical methods of equation solution, Appl. Math. Comput., 186, 665–669, 2007.
  • 5. E. Babolian, Sh. Javadi, H. Sadeghi, Restarted Adomian method for integral equations, Appl. Math. Comput., 153, 353–359, 2004.
  • 6. H. Jafari, V.D. Gejji, Revised Adomian decomposition method for solving a system of nonlinear equations, Appl. Math. Comput., 175, 1–7, 2006.
  • 7. K. Al-Khaled, F.M. Allan, Construction of solutions for the shallow water equations by the decomposition method, Math. Comput. Simul., 66, 479–486, 2004.
  • 8. D. Kaya, I.E. Inan, Exact and travelling wave solutions for nonlinear coupled equations using symbolic computations, Appl. Math. Comput., 151, 775–787, 2004.
  • 9. F.M. Allan, K. Al-Khaled, An approximation of the analytic solution of the shock wave equation, J. Comput. Appl. Math., 192, 301–309, 2006.
  • 10. E. Az-Zo’bi, K. Al-Khaled, A new convergence proof of the Adomian decomposition method for a mixed hyperbolic elliptic system of conservation laws, Appl. Math. Comput., 217, 4248–4256, 2010.
  • 11. Y. Cherrualt, Convergence of Adomian’s method, Kybernetes, 18, 31–38, 1989.
  • 12. Y. Cherrualt, G. Adomian, Decomposition methods: A new proof of convergence,Math. Comput. Model., 18, 103–106, 1993.
  • 13. M. M. Hosseini, H. Nasabzaded, On the convergence of Adomian decomposition method, Appl. Math. Comput., 182, 536–543, 2006.
  • 14. D. Kaya, I.E. Inan, A convergence analysis of the ADM and an application, Appl. Math. Comput., 161, 1015–1025, 2005.
  • 15. A.M. Wazwaz, The decomposition method applied to systems of partial differential equations and to the reaction-diffusion Brusselator model, Appl Math Comput., 110, 2–3, 251–64, 2000.
  • 16. A.M. Wazwaz, The numerical solution of sixth-order boundary value problems by the modified decomposition method, Appl. Math. Comput., 118, 3, 11–25, 2001.
  • 17. N. Ngarhasta, B. Some, K. Abbaoui, Y. Cherrualt, New numerical study of Adomian method applied to a diffusion model, Kybernetes, 31, 61–75, 2002.
  • 18. T.L. Saaty, J. Bram, Nonlinear Mathematics, McGraw-Hill, New York, 1964.
  • 19. G. Adomian, R.E. Meyers, Isentropic flow of an inviscid gas, Appl. Math. Lett., 8, 1, 43–46, 1995.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-f6b2bed7-b679-4cff-b3db-186feeea5b07
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