Approximate analytical solutions of fractional gas dynamic equations

Applied Mathematics and Computation

Volumn 217, Issue 24, 2011, Pages 9905-9915

  Das, S ^a   Kumar, R ^a  

^a BANARAS HINDU UNIVERSITY   (India)

Author keywords

Caputo derivative; Differential transforms method; Fractional Brownian motion; Fractional order PDEs

Indexed keywords

APPROXIMATE ANALYTICAL SOLUTIONS; CAPUTO DERIVATIVES; CLASSICAL EQUATION; COMPUTATIONAL WORK; DIFFERENTIAL TRANSFORM; DIFFERENTIAL TRANSFORM METHOD; FRACTIONAL BROWNIAN MOTION; FRACTIONAL ORDER; GASDYNAMIC EQUATIONS; NON-HOMOGENEOUS; NUMERICAL RESULTS; SERIES SOLUTIONS; SHALLOW WATER EQUATIONS; TIME DERIVATIVE;

BROWNIAN MOVEMENT; EQUATIONS OF MOTION; GAS DYNAMICS; MATHEMATICAL TRANSFORMATIONS; PARTIAL DIFFERENTIAL EQUATIONS; TEMPERATURE CONTROL;

NONLINEAR EQUATIONS;

EID: 79959205476     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2011.03.144     Document Type: Article

References (42)

1. J.L. Steger, and R.F. Warming Flux vector splitting of the inviscid gas dynamic equations with application to finite-difference methods J. Comput. Phys. 40 1981 263 293
2. T.G. Elizarova, Quasi-gas dynamics equations, ISBN: 978-3-642-00291-5, Springer Verlag (2009).
3. W.F. Ames Nonlinear Partial Differential Equations in Engineering 1965 Academic Press Inc
4. D.J. Evans, and H. Bulut A new approach to the gas dynamic equations, An application of the decomposition method Int. J. Comput. Math. 79 2002 817 822 (Pubitemid 41710621)
5. A.D. Polyanin, V.F. Zaitsev, Handbook of nonlinear partial differential equations, ISBN- 9781584883555, CRC Press, Taylor and Francis Group (2004).
6. A. Aziz, and D. Anderson The use of pocket computer in gas dynamics Comput. Educat. 9 1985 41 56
7. T-P.Liu, Nonlinear Waves in Mechanics and Gas Dynamics, Defense Technical Information Center, Accession Number: ADA 238340 (1990).
8. M. Rasulov, and T. Karaguler Finite difference schemes for solving system equations of gas dynamic in a class of discontinuous functions Appl. Math. Comput. 143 2003 45 164
9. G.B. Whitham Variational method and applications to water wave Proc. Roy. Soc. Lond. 229 1967 6 25
10. L.J. Broer Approximate equations for long wave waves Appl. Sci. Res. 31 1975 377 395
11. D.J.A. Kaup Higher order water wave equation and the method for solving it Proc. Theor. Phys. 54 1975 396 408
12. N. Crnjaric-Zic, S. Vukovic, and L. Sopta Ballanced finite volume WENO and central WENO schemes for the shallow water and the open channel flow equations J. Comput. Phys. 200 2004 512 548 (Pubitemid 39435998)
13. A. Bermudez, and M.E. Vazquez Upwind methods for hyperbolic conservation laws with source terms Comput. Fluids 23 1994 1049
14. J. Burguete, and P. Garcia-Navarro Efficient construction of high resolution TVD conservative schemes for equations with source terms: application to shallow-water flows Int. J. Numer. Meth. Fluids 37 2001 209
15. M.E. Hubbard, and P. Garcia- Navarro Flux difference splitting and the balancing of source terms and flux gradient J. Comput. Phys. 165 2000 89
16. T. Gallouet, J.M. Herard, and N. Seguin Some approximate Godunov schemes to compute shallow water equations with topography Comput. Fluids 32 2003 479
17. P. Garcia- Navarro, and M.E. Vazquez-Cendon On numerical treatment of the source term in shallow water equations Comput. Fluids 29 2000 951
18. I. Podlubny Fractional Differential Equations 1999 Academic Press New York
19. R. Hilfer Applications of Fractional Calculus in Physics 1999 Academic press Orlando
20. A.A. Kilbas, H.M. Srivastava, and J.J. Trujillo Theory and Applications of Fractional Differential Equations 2006 Elsevier
21. S. Das A note on fractional diffusion equations Chaos Soliton. Fract. 42 2009 2074 2079
22. J.K. Zhou Differential Transformation and its Applications for Electrical Circuits 1986 Huazhong University Press Wuhan, China in Chinese
23. M.J. Jang, C.L. Chen, and Y.C. Liu Two dimensional differential transform for Partial differential equations Appl. Math. Comput. 121 2001 261 270
24. F. Ayaz On the two-dimensional differential transform method Appl. Math. Comput. 143 2003 361 374
25. L.T. Yu, and C.K. Chen Application of Taylor transformation to optimize rectangular fins with variable thermal parameters Appl. Math. Model. 22 1998 11 21
26. L.T. Yu, and C.K. Chen The solution of the Blasius equation by the differential transformation method Math. Comput. Model. 28 1998 101 111
27. C.L. Chen, and Y.C. Liu Differential transformation technique for steady nonlinear heat conduction problems Appl. Math. Comput. 95 1998 155 164
28. J.H. Ahmad Efficiency of differential transform method for Genesio system J. Math. Stat. 5 2009 93 96
29. L. Zou, Z. Zong, Z. Wang, and S. Tian Differential transform method for solving solitary wave with discontinuity Phys. Lett. A 374 2010 3451 3454
30. H. Jafari, C. Chun, S. Seifi, and M. Saeidy Analytical solution for nonlinear gas dynamic homotopy analysis method Appl. Appl. Math. Int. J. 4 2009 149 154
31. H. Jafari, M. Alipour, and H. Tajadodi Two-dimensional differential transform method for solving nonlinear partial differential equations Int. J. Res. Rev. Appl. Sci. 2 2010 47 52
32. F.M. Allan, and K. Al-Khaled An approximation of the analytic solution of the shock wave equation J. Comput. Appl. Math. 192 2006 301 309
33. I. Khatami, N. Tolou, J. Mahmoudi, and M. Rezvani Application of homotopy analysis method and variational iteration method for shock wave equation J. Appl. Sci. 8 2008 848 853
34. M.E. Berberler, and A. Yildirim He's homotopy perturbation method for solving the shock wave equation Appl. Anal. 88 2009 997 1004
35. F. Xie, Z. Yan, and H. Zhang Explicit and exact travelling wave solutions of WBK shallow water equations Phys. Lett. A 285 2001 76 80 (Pubitemid 32607164)
36. D.D. Ganji, H.B. Rokni, M.G. Sfahani, and S.S. Ganji Approximate travelling wave solutions for coupled WBK shallow water Adv. Eng. Software 41 2010 956 961
37. M.M. Rashidi, and E. Erfani Travelling wave solutions of WBK shallow water equations by differential transform method Adv. Theor. Appl. Mech. 3 2010 263 271
38. J. Liu, and G. Hou Numerical solutions of the space and time fractional coupled Burgers equations by generalized differential transform method Appl. Math. Comput. 217 2011 7001 7008
39. Z. Odibat, S. Momani, and V.S. Erturk Generalized differential transform method: for solving a space- and time-fractional diffusion-wave equation Phys Lett. A 370 2007 379 387
40. S. Momani, Z. Odibat, and V.S. Erturk Generalized differential transform method: application to differential equations of fractional order Appl. Math. Comput. 19 2008 467 477 (Pubitemid 351273764)
41. Z. Odibat, and S. Momani A generalized differential transform method for linear partial differential equations of fractional order Appl. Math. Lett. 21 2008 94 199
42. Z. Odibat, and N. Shawagfeh Generalized Taylor's formula Appl. Math. Comput. 186 2007 286 293 (Pubitemid 46435616)