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The solution of nonlinear coagulation problem with mass loss

Author

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  • Abulwafa, E.M.
  • Abdou, M.A.
  • Mahmoud, A.A.

Abstract

The coagulation problem, which is an important process in many different scientific fields, is described as a nonlinear problem. Through this work, the nonlinear coagulation problem with linear continuous mass loss is solved using two different techniques, the Adomian’s decomposition method and the He’s variational-iteration method. The solution of the problem is carried-out for two different kernels and different initial conditions. The calculations are carried out for different values of the mass loss coefficient. He’s variational-iteration method is easier than the Adomian’s decomposition method and it is introduced to overcome the difficulty arising in calculating Adomian’s polynomials.

Suggested Citation

  • Abulwafa, E.M. & Abdou, M.A. & Mahmoud, A.A., 2006. "The solution of nonlinear coagulation problem with mass loss," Chaos, Solitons & Fractals, Elsevier, vol. 29(2), pages 313-330.
    • Handle: RePEc:eee:chsofr:v:29:y:2006:i:2:p:313-330
    DOI: 10.1016/j.chaos.2005.08.044
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    Cited by:

    1. Dehghan, Mehdi & Tatari, Mehdi, 2008. "Identifying an unknown function in a parabolic equation with overspecified data via He’s variational iteration method," Chaos, Solitons & Fractals, Elsevier, vol. 36(1), pages 157-166.
    2. Gordoa, P.R., 2007. "A note on solutions of an equation modelling arterial deformation," Chaos, Solitons & Fractals, Elsevier, vol. 33(5), pages 1505-1511.
    3. Memarbashi, Reza, 2008. "Numerical solution of the Laplace equation in annulus by Adomian decomposition method," Chaos, Solitons & Fractals, Elsevier, vol. 36(1), pages 138-143.
    4. Javidi, M. & Golbabai, A., 2008. "Exact and numerical solitary wave solutions of generalized Zakharov equation by the variational iteration method," Chaos, Solitons & Fractals, Elsevier, vol. 36(2), pages 309-313.
    5. Goh, S.M. & Noorani, M.S.M. & Hashim, I., 2009. "A new application of variational iteration method for the chaotic Rössler system," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1604-1610.
    6. Javidi, M. & Golbabai, A., 2009. "A new domain decomposition algorithm for generalized Burger’s–Huxley equation based on Chebyshev polynomials and preconditioning," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 849-857.
    7. Javidi, M. & Golbabai, A., 2009. "Modified homotopy perturbation method for solving non-linear Fredholm integral equations," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1408-1412.
    8. Batiha, B. & Noorani, M.S.M. & Hashim, I., 2008. "Application of variational iteration method to the generalized Burgers–Huxley equation," Chaos, Solitons & Fractals, Elsevier, vol. 36(3), pages 660-663.
    9. Abdel-Halim Hassan, I.H., 2008. "Comparison differential transformation technique with Adomian decomposition method for linear and nonlinear initial value problems," Chaos, Solitons & Fractals, Elsevier, vol. 36(1), pages 53-65.
    10. Lu, Junfeng, 2009. "He’s variational iteration method for the modified equal width equation," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2102-2109.
    11. Wazwaz, Abdul-Majid, 2008. "A study on linear and nonlinear Schrodinger equations by the variational iteration method," Chaos, Solitons & Fractals, Elsevier, vol. 37(4), pages 1136-1142.
    12. Golbabai, A. & Javidi, M., 2009. "A spectral domain decomposition approach for the generalized Burger’s–Fisher equation," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 385-392.

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