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Application of Optimal Homotopy Asymptotic Method with Daftardar-Jafari Polynomials to Couple System of Boussinesq Equations

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Abstract

The solitary wave results of many Boussinesq systems of equations are gained by using the Optimal Homotopy Asymptotic method with Daftardar-Jafari Polynomials. The results were intended in the form of a convergent power series with simply predictable components. The convergence of the method is well-known numerically for the system with several initial values. The current procedure completes particularly well in relations of exactness a perseverance.

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References

  1. Ha, S.N.: A nonlinear shooting method for two-point boundary value problems. Comput. Math. Appl. 42(10), 1411–1420 (2001)

    Article  MathSciNet  Google Scholar 

  2. Osborne, M.R.: On shooting methods for boundary values problems. J. Math. Anal. Appl. 27(2), 417–433 (1969)

    Article  MathSciNet  Google Scholar 

  3. Butcher, J. C. (1987). The numerical analysis of ordinary differential equations: Rung-Kutta and general linear methods. Wiley-Interscience.

  4. Hu, H.Y., Li, Z.C.: Collocation methods for Poisson’s equation original research article. Comput. Methods Appl. Mech. Eng. 195, 4139–4160 (2006)

    Article  Google Scholar 

  5. Ahmad, H., Khan, T.A., Ahmad, I., Stanimirović, P.S., Chu, Y.M.: A new analyzing technique for nonlinear time fractional Cauchy reaction-diffusion model equations. Results Phys. 19, 103462 (2020)

    Article  Google Scholar 

  6. H. Ahmad, A. Akgül, T.A. Khan, P.S. Stanimirović and Y.M. Chu, New perspective on the conventional solutions of the nonlinear time-fractional partial differential equations, Complex., 2020,|Article ID 8829017, (2020).

  7. Fang, Q., Tsuchiya, T., Yamamoto, T.: Finite difference, finite element and finite volume methods applied to two-point boundary value problems. J. Comput. Appl. Math. 139(1), 9–19 (2002)

    Article  MathSciNet  Google Scholar 

  8. Dehghan, M.: Weighted finite difference techniques for the one dimensional advection-diffusion equation. Appl. Math. Comput. 147(2), 307–319 (2004)

    MathSciNet  MATH  Google Scholar 

  9. Li, J.F., Ahmad, I., Ahmad, H., Shah, D., Chu, Y.M., Thounthong, P., Ayaz, M.: Numerical solution of two-term time-fractional PDE models arising in mathematical physics using local meshless method. Open Physics. 18(1), 1063–1072 (2020)

    Article  Google Scholar 

  10. Inc, M., Khan, M.N., Ahmad, I., Yao, S.W., Ahmad, H., Thounthong, P.: Analysing time-fractional exotic options via efficient local meshless method. Results Phys. 19, 103385 (2020)

    Article  Google Scholar 

  11. Ihlenburg, F., Babuška, I.: Finite element solution of the Helmholtz equation with high wave number. Comput. Math. Appl. 30(9), 9–37 (1995)

    Article  MathSciNet  Google Scholar 

  12. Hwon, Y.W., Bank, H.: The finite element method using MATLAB. CRC Press, New York (1996)

    Google Scholar 

  13. Ahmad, H., Seadawy, A.R., Khan, T.A., Thounthong, P.: Analytic approximate solutions for some nonlinear Parabolic dynamical wave equations. J. Taibah Univer. Sci. 14(1), 346–358 (2020)

    Article  Google Scholar 

  14. Ahmad H, Alam N, Omri M. New computational results for a prototype of an excitable system. Results in Physics. 2021 Aug 11:104666.

  15. Liao, S.J.: A kind of linearity-invariance under homotopy and some simple applications of it in mechanics. Technical Report 520. Institute of Shipbuilding, University of Hamburg, Hamgburg (1992)

    Google Scholar 

  16. Gupta, A.K., Ray, S.S.: Comparison between Homotopy Perturbation Method and Optimal Homotopy Asymptotic Method for the Soliton Solutions of Boussinesq-Burger Equations. Comput. Fluids 103, 34–41 (2014)

    Article  MathSciNet  Google Scholar 

  17. N.Herisanu,V. Marinca,(2012). ). An Optimal Homotopy Perturbation Method for a non-Conservative Dynamical System of a Rotating Electrical Machine, Zeitschrift FUR Naturforschung Section A-A JOURNAL OF Physical Sciences,67(8–9),509–516.

  18. Marinca, V., Herisanu, N.: Application of Optimal Homotopy Asymptotic Method for solving nonlinear equations arising in heat transfer. Int, s in Heat and Mass Transfer 35, 710–715 (2008)

    Article  Google Scholar 

  19. Marinca, V., Herisanu, N., Bota, C., Marinca, B.: An Optimal Homotopy Asymptotic Method applied to steady flow of a fourth-grade fluid past a porous plate. App, Mathe, Letters 22, 245–251 (2009)

    Article  MathSciNet  Google Scholar 

  20. Herisanu, N., Marinca, V., Dordea, T., Madescu, G.: A new analytical approach to nonlinear vibration of an electric machine. Proc. Romanian Acad. Series A: Math. Phy. Tech. Sci. Inf. Sci. 9, 229–236 (2008)

    Google Scholar 

  21. Herisanu, N., Marinca, V.: An Optimal Homotopy Asymptotic Method with application of thin film flows. Cent. Eur. J. Phys. 6(3), 648–653 (2008)

    Google Scholar 

  22. Al-Hayani, W.: Daftardar-Jafari Method for Fractional Heat-Like and Wave-Like equations with Variable Coefficients. Appl. Math. 8, 215–228 (2017)

    Article  Google Scholar 

  23. Ullah, I., Rahim, M.T. and Khan, H.: Application of Daftardar Jafari method to first grade MHD squeezing fluid flow in a porous medium with slip boundary condition, Article ID 479136, 8 pages (2014)

  24. Ali, J., Shah, S., Islam, S., Khan, H.: Application of optimal homotopy asymtotic method with daftardar-jeffery polynomials to non-linear differential equations. World Appl. Sci. J. 28, 1456–1462 (2013)

    Google Scholar 

  25. Ullah, H., Nawaz, R., Islam, S., Idrees, M., Fiza, M.: The optimal homotopy asymptotic method with application to modified Kawahara equation. J. Assoc. Arab Univ. Basic Appl. Sci. 18, 82–88 (2015)

    Google Scholar 

  26. Shah, Z., Nawaz, R., Shah, S., Shah, S.I.A., Shah, M.: Use of the Daftardar-Jeffery polynomials in optimal homotopy asymptotic method for the solution of linear and nonlinear Klein-Gordon equations. J. App. Environ. Biol. Sci. 6, 71–81 (2016)

    Google Scholar 

  27. Sachs, R.L.: on the integrable variant of the Boussinesq system: Painlevé Property rational solutions, a related many-body system, and equivalence with the AKNS Hierarchy. Physica D 30, 1–27 (1988)

    Article  MathSciNet  Google Scholar 

  28. Fan, E.: extended tanh-function method and its applications to nonlinear equations. Phys. Lett. A 277, 212–218 (2000)

    Article  MathSciNet  Google Scholar 

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Hussain, Z., Nawaz, R., Ayaz, M. et al. Application of Optimal Homotopy Asymptotic Method with Daftardar-Jafari Polynomials to Couple System of Boussinesq Equations. Int. J. Appl. Comput. Math 8, 44 (2022). https://doi.org/10.1007/s40819-021-01221-0

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