DOI QR코드

DOI QR Code

ANALYTIC TREATMENT FOR GENERALIZED (m + 1)-DIMENSIONAL PARTIAL DIFFERENTIAL EQUATIONS

  • AZ-ZO'BI, EMAD A. (DEPARTMENT OF MATHEMATICS AND STATISTICS, MUTAH UNIVERSITY)
  • Received : 2018.04.11
  • Accepted : 2018.12.19
  • Published : 2018.12.25

Abstract

In this work, a recently developed semi-analytic technique, so called the residual power series method, is generalized to process higher-dimensional linear and nonlinear partial differential equations. The solutions obtained takes a form of an infinite power series which can, in turn, be expressed in a closed exact form. The results reveal that the proposed generalization is very effective, convenient and simple. This is achieved by handling the (m+1)-dimensional Burgers equation.

References

  1. O. Abu Arqub, Z. Abo-Hammour, R. Al-Badarneh and S. Momani, A reliable analytical method for solving higher-oder initial value problems, Discrete Dynamics in Nature and Society (2013).
  2. H. Tariq and G. Akram, Residual power series method for solving time-space-fractional Benney-Lin equation arising in falling film problems, J. Appl. Math. Comput. 55 (1-2) (2017), 683-708. https://doi.org/10.1007/s12190-016-1056-1
  3. A. Kumar and S. Kumar, Residual power series method for fractional Burger types equations, Nonlinear Engineering, 5 (4) (2016).
  4. A. El-Ajoua, O. Abu Arqub and M. Al-Smadi, A general form of the generalized Taylors formula with some applications, Applied Mathematics and Computation (256) (1) (2015), 851-859. https://doi.org/10.1016/j.amc.2015.01.034
  5. E. A. Az-Zo'bi, Exact analytic solutions for nonlinear diffusion equations via generalized residual power series method, International Journal of Mathematics and Computer Science 14 (1) (2019), 69-78.
  6. A. Jabbari, H. Kheiri and A. Yildirim, Homotopy analysis and homotopy Pad methods for (1+1) and (2+1)-dimensional dispersive long wave equations, International Journal of Numerical Methods for Heat & Fluid Flow, 23 (4) (2013), 692-706. https://doi.org/10.1108/09615531311323818
  7. V. K. Srivastava, M. K. Awasthi and R. K. Chaurasia, Reduced differential transform method to solve two and three dimensional second order hyperbolic telegraph equations, Journal of King Saud University - Engineering Sciences, 29 (2017), 166-171.
  8. E. A. Az-Zo'bi and M. M. Qousini, Modified Adomian-Rach decomposition method for solving nonlinear time-dependent IVPs, Appl. Math. Sci., 11 (8) (2017), 387-395. https://doi.org/10.12988/ams.2017.714
  9. B. Lin and K. Li, The (1+3)-dimensional Burgers equation and its comparative solutions, Computers and Mathematics with Applications 60 (2010) 3082-3087. https://doi.org/10.1016/j.camwa.2010.10.009
  10. V. K. Srivastava, M. K. Awasthi, (1+ n)-Dimensional Burgers equation and its analytical solution: A comparative study of HPM, ADM and DTM, Ain Shams Engineering Journal - Engineering Physics and Mathematics 5 (2014), 533-541. https://doi.org/10.1016/j.asej.2013.10.004
  11. E. A. Az-Zo'bi, On the Reduced Differential Transform Method and its Application to the Generalized Burgers-Huxley Equation, Applied Mathematical Sciences, 8 (177) (2014), 8823-8831. https://doi.org/10.12988/ams.2014.410835
  12. R. G. Bartle and D. R. Sherbert, Introduction to Real Analysis (4th ed.), Wiley, 2011.
  13. F. J. Alexander and J. L. Lebowitz, Driven diffusive systems with a moving obstacle: a variation on the Brazil nuts problem, J. Phys. 23 (1990), 375-382.
  14. F. J. Alexander and J. L. Lebowitz, On the drift and diffusion of a rod in a lattice fluid, J. Phys. 27 (1994) 683-696.