Haar wavelet-based numerical investigation of coupled viscous Burgers' equation

References

• T.A. Abassy, M.A. El-Tawil, and H. El-Zoheiry, Exact solutions of some nonlinear partial differential equations using the variational iteration method linked with Laplace transforms and the Pade technique, Comput. Math. Appl. 54 (2007), pp. 940–954. doi: 10.1016/j.camwa.2006.12.067
   Web of Science ®Google Scholar
• M.A. Abdou and A.A. Soliman, Variational iteration method for solving Burgers’ and coupled Burgers’ equations, J. Comput. Appl. Math. 181 (2005), pp. 245–251. doi: 10.1016/j.cam.2004.11.032
   Web of Science ®Google Scholar
• H. Aminikhah, Approximate analytical solution for the systems of variable-coefficient coupled Burgers’ equation, J. Interpolation Approx. Sci. Comput. 2013 (2013), pp. 1–9. doi: 10.5899/2013/jiasc-00039
   Google Scholar
• A.R. Bahadir, A fully implicit finite-difference scheme for two dimensional Burgers’ equation, Appl. Math. Comput. 137 (2003), pp. 131–137. doi: 10.1016/S0096-3003(02)00091-7
   Web of Science ®Google Scholar
• J.M. Burgers, A mathematical model illustrating the theory of turbulence, Adv. Appl. Mech. 1 (1948), pp. 171–199. doi: 10.1016/S0065-2156(08)70100-5
   Google Scholar
• C. Chen and C. Hsiao, Haar wavelet method for solving lumped and distributed-parameter systems, IEE Proc. Control Theory Appl. 144 (1997), pp. 87–94. doi: 10.1049/ip-cta:19970702
   Google Scholar
• C.I. Christov, A complete orthogonal system of functions in L2(R) space, SIAM J. Appl. Math. 42 (1982), pp. 1337–1344. doi: 10.1137/0142093
   Web of Science ®Google Scholar
• M. Dehghan, H. Asgar, and S. Mohammad, The solution of coupled Burgers’ equations using Adomian-Pade technique, Appl. Math. Comput. 189 (2007), pp. 1034–1047. doi: 10.1016/j.amc.2006.11.179
   Web of Science ®Google Scholar
• S.E. Esipov, Coupled Burgers’ equations: A model of poly dispersive sedimentation, Phys. Rev. E 52 (1995), pp. 3711–3718. doi: 10.1103/PhysRevE.52.3711
   PubMed Web of Science ®Google Scholar
• C.H. Hsiao, Numerical solution of stiff differential equations via Haar wavelets, Int. J. Comput. Math. 82 (2005), pp. 1117–1123. doi: 10.1080/00207160512331323308
   Web of Science ®Google Scholar
• P.C. Jain and D.N. Holla, Numerical solution of coupled Burgers’ equations, Int. J. Numer. Methods Eng. 12 (1978), pp. 213–222.
   Web of Science ®Google Scholar
• H. Kaur, R.C. Mittal, and V. Mishra, Haar wavelet quasilinearization approach for solving nonlinear boundary value problems, Am. J. Comput. Math. 1 (2011), pp. 176–182. doi: 10.4236/ajcm.2011.13020
   Google Scholar
• H. Kaur, R.C. Mittal, and V. Mishra, Haar wavelet approximate solutions for the generalized Lane Emden equations arising in astrophysics, Comput. Phys. Commun. 184 (2013), pp. 2269–2277. doi: 10.1016/j.cpc.2013.04.013
   Web of Science ®Google Scholar
• H. Kaur, R.C. Mittal, and V. Mishra, Numerical Solution of a Laminar Viscous Flow Boundary Layer Equation Using Uniform Haar Wavelet Quasi-linearization Method, Proceedings of Conference World Academy of Sciences, Engineering and Technology, ICMCSSE-2013, Zurich, Switzerland, Vol. 79, 2013, pp. 1410–1415.
   Google Scholar
• D. Kaya, An explicit solution of coupled viscous Burgers’ equation by the Decomposition method, Int. J. Math. Math. Sci. 27 (2001), pp. 675–680. doi: 10.1155/S0161171201010249
   Google Scholar
• S. Kestler and R. Stevenson, An efficient approximate residual evaluation in the adaptive tensor product wavelet method, J. Sci. Comput. 57 (2013), pp. 439–463. doi: 10.1007/s10915-013-9712-1
   Web of Science ®Google Scholar
• S. Kutluay and Y. Ucar, Numerical solutions of the coupled Burgers’ equation by the Galerkin quadratic B-spline finite element method, Math. Methods Appl. Sci. 36 (2013), pp. 2403–2415. doi: 10.1002/mma.2767
   Web of Science ®Google Scholar
• R.C. Mittal and G. Arora, Numerical solution of the coupled viscous Burgers’ equation, Commun. Nonlinear Sci. Numer. Simul. 16 (2011), pp. 1304–1313. doi: 10.1016/j.cnsns.2010.06.028
   Web of Science ®Google Scholar
• R.C. Mittal and S. Kumar, Numerical study of Fisher's equation by wavelet Galerkin method, Int. J. Comput. Math. 83 (2006), pp. 287–298. doi: 10.1080/00207160600717758
   Web of Science ®Google Scholar
• J. Nee and J. Duan, Limit set of trajectories of the coupled viscous Burgers’ equations, Appl. Math. Lett. 11 (1998), pp. 57–61. doi: 10.1016/S0893-9659(97)00133-X
   Web of Science ®Google Scholar
• A. Rashid and A.I.B. Ismail, A Fourier pseudo spectral method for solving coupled viscous Burgers’ equations, Comput. Methods Appl. Math. 9 (2009), pp. 412–420. doi: 10.2478/cmam-2009-0026
   Google Scholar
• V.K. Srivastava, S. Singh, and M.K. Awasthi, Numerical solutions of coupled Burgers’ equations by an implicit finite difference scheme, Am. Inst. Phys. Adv. 3 (2013), pp. 082131-1–082131-7.
   Google Scholar
• N.H. Sweilam and M.M. Khader, Exact solutions of some coupled nonlinear partial differential equations using the homotopy perturbation method, Comput. Math. Appl. 58 (2009), pp. 2134–2141. doi: 10.1016/j.camwa.2009.03.059
   Web of Science ®Google Scholar
• W. Sweldens, The construction and application of wavelets in numerical analysis, Ph.D. thesis, 1995. Available at http://cm.bell-labs.com/cm/cs/who/wim/thesis/thesis.pdf.
   Google Scholar