Skip to main content
SpringerLink
Log in

Reduced differential transform method for solving parabolic-like and hyperbolic-like equations

  • Published:
SeMA Journal Aims and scope Submit manuscript

Abstract

In this paper, we present the exact solutions of the partial differential equations in different dimensions with variable coefficients by using reduced differential transform method (RDTM). The advantage of this method is that, it solves the problem directly without the need for linearization, perturbation, or any other transformation, gives the solution in the form of convergent power series with elegantly computed components. Therefore, the solution procedure of the RDTM is simpler than other traditional methods. This method can successfully be applied to solve the heat-like and wave-like equations with variable coefficients.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Akhmetov, A.A.: Long current loops as regular solutions of the equation for coupling currents in a flat two-layer superconducting cable. Cryogenics 43(3–5), 317–322 (2003)

    Article  Google Scholar 

  2. Alomari, A.K., Noorani, M.S.M., Nazar, R.: Solutions of heat-like and wave-like equations with variable coefficients by means of the homotopy analysis method. Chin. Phys. Lett. 25(2), 589–592 (2008)

    Article  Google Scholar 

  3. Wazwaz, A.M.: Exact solutions for heat-like and wave-like equations with variable coefficients. Appl. Math. Comput. 149, 15–29 (2004)

    MathSciNet  MATH  Google Scholar 

  4. Secer, A.: Approximate analytic solution of fractional heat-like and wave-like equations with variable coefficients using the differential transforms method. Adv. Differ. Equ. 2012, 198 (2012)

    Article  MathSciNet  Google Scholar 

  5. Shou, D., He, J.H.: Beyond Adomian method: the variational iteration method for solving heat-like and wave-like equations with variable coefficients. Phys. Lett. A 372(3), 233–237 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  6. Manolis, G., Rangelov, T.: Non-homogeneous elastic waves in solid: notes on the vector decomposition technique. Soil Dyn. Earthq. Eng. 26, 952–959 (2006)

    Article  Google Scholar 

  7. Lin, J.: Homotopy perturbation method for solving partial differential equations with variable coefficients. Int. J. Contemp. Math. Sci. 3(28), 1395–1407 (2008)

    MathSciNet  MATH  Google Scholar 

  8. Tabatabaei, K., Celik, E., Tabatabaei, R.: The differential transform method for solving heat-like and wave-like equations with variable coefficients. Turk. J. Phys. 36, 87–98 (2012)

    Google Scholar 

  9. Abdou, M.A.: Approximate solutions of system of PDEEs arising in physics. Int. J. Nonlinear Sci. 12(3), 305–312 (2011)

    MathSciNet  MATH  Google Scholar 

  10. Al-Amr, M.O.: New applications of reduced differential transform method. Alex. Eng. J. 53, 243–247 (2014)

    Article  Google Scholar 

  11. Rawashdeh, M., Obeidat, N.A.: On finding exact and approximate solutions to some PDEs using the reduced differential transform method. Appl. Math. Inf. Sci. 8(5), 2171–2176 (2014)

    Article  MathSciNet  Google Scholar 

  12. Rawashdeh, M.: Using the reduced differential transform method to solve nonlinear PDEs arises in biology and physics. World Appl. Sci. J. 23(8), 1037–1043 (2013)

    Google Scholar 

  13. Sohail, M., Mohyud-Din, S.T.: Reduced differential transform method for parabolic PDES. Int. J. Modern Eng. Sci. 1(2), 80–87 (2012)

    Google Scholar 

  14. Taghizadeh, N., Moosavi Noori, S.R.: Exact solutions of the cubic nonlinear Schrödinger equation with a trapping potential by reduced differential transform method. Math. Sci. Lett. 5(3):1–5 (2016)

  15. Oderinu, R.A.: The reduced differential transform method for the exact solutions of Advection, Burgers and coupled Burgers equations, Theory. Theory Appl. Math. Comput. Sci. 2(1), 10–14 (2012)

    MathSciNet  MATH  Google Scholar 

  16. Ahmed, S.E., Elzaki, T.M.: Solution of heat and wave-like equations by adomian decomposition sumudu transform method. Br. J. Math. Comput. Sci. 8(2), 101–111 (2015)

    Article  Google Scholar 

  17. Keskin, Y. Ph.D Thesis, Selcuk University, in Turkish (2010)

  18. Keskin, Y., Oturance, G.: Reduced differential transform method for partial differential equations. Int. J. Nonlinear Sci. Numer. Simul. 10(6), 741–749 (2009)

    Article  Google Scholar 

  19. Keskin, Y., Oturance, G.: Reduced differential research transform method for fractional partial differential equations. Nonlinear Sci. Lett. A 1(1), 61–72 (2010)

    Google Scholar 

  20. Keskin, Y., Oturance, G.: Application of reduced differential transformation method for solving gas dynamics equation. Int. J. Contemp. Math. Sci. 5(22), 1091–1096 (2010)

    MathSciNet  MATH  Google Scholar 

  21. Gazizov, R.K.: Lie algebras of approximate symmetries. Nonlinear Math. Phys. 3(1–2), 96–101 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  22. Ibragimov Ed. N.H. CRC Handbook of Lie Group Analysis of Differential Equations, vol. 1: Symmetries, Exact Solutions, and Conservation Laws, CRC Press, Boca Raton, FL (1994)

  23. Ibragimov, N.H.: CRC Handbook of lie group analysis of differential equations, vol. 2: Applications in Engineering and Physical Sciences, CRC Press, Boca Raton, FL (1995)

  24. Ibragimov, N.H.: CRC handbook of lie group analysis of differential equations, vol. 3: New Trends in Theoretical Development and Computational Methods (1996)

  25. Ruggieri, M., Valenti, A.: Approximate symmetries in nonlinear viscoelastic media. Bound. Value Probl. 2013, 143 (2013)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Faculty of Mathematical Sciences, University of Guilan, P.O.Box 1914, Rasht, Iran

    N. Taghizadeh & S. R. Moosavi Noori

Authors
  1. N. Taghizadeh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. R. Moosavi Noori
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. R. Moosavi Noori.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Taghizadeh, N., Noori, S.R.M. Reduced differential transform method for solving parabolic-like and hyperbolic-like equations. SeMA 74, 559–567 (2017). https://doi.org/10.1007/s40324-016-0101-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40324-016-0101-1

Keywords

Mathematics Subject Classification

Search

Navigation