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An efficient numerical method for solving nonlinear foam drainage equation

Indian Journal of Physics volume 92, pages 231–243 (2018)Cite this article

Abstract

In this paper, the nonlinear foam drainage equation, which is a famous nonlinear partial differential equation, is solved by using a hybrid numerical method based on the quasilinearization method and the bivariate generalized fractional order of the Chebyshev functions (B-GFCF) collocation method. First, using the quasilinearization method, the equation is converted into a sequence of linear partial differential equations (LPD), and then these LPDs are solved using the B-GFCF collocation method. A very good approximation of solutions is obtained, and comparisons show that the obtained results are more accurate than the results of other researchers.

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Abbreviations

u(x, t):

Unknown function

\(\bar{u}(x,t)\) :

The approximate solution

\(\psi (x,t)\) :

Plateau border

\(_\eta FT_n^\alpha \) :

Basis functions

m :

The number of basis functions

\(E_A\) :

The maximum of the absolute error

t :

Time position coordinate

x :

Scaled coordinate

\(\eta \) :

Length of the domain of function

\(\alpha \) :

The order of basis functions

\(\mathbf{K }\) :

Unknown coefficients matrix

\(\varPhi (t)\) :

The vector of basis functions

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Author information

Authors and Affiliations

  1. Department of Computer Sciences, Shahid Beheshti University, G.C., Tehran, Iran

    Kourosh Parand & Mehdi Delkhosh

  2. Department of Cognitive Modelling, Institute for Cognitive and Brain Sciences, Shahid Beheshti University, G.C., Tehran, Iran

    Kourosh Parand

Authors
  1. Kourosh Parand
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  2. Mehdi Delkhosh
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Corresponding author

Correspondence to Kourosh Parand.

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Cite this article

Parand, K., Delkhosh, M. An efficient numerical method for solving nonlinear foam drainage equation. Indian J Phys 92, 231–243 (2018). https://doi.org/10.1007/s12648-017-1098-8

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  • DOI: https://doi.org/10.1007/s12648-017-1098-8

Keywords

  • Foam drainage equation
  • Fractional order of the Chebyshev functions
  • Quasilinearization method
  • Collocation method
  • Nonlinear PDE

PACS Nos.

  • 02.30.Jr
  • 02.70.Hm
  • 82.70.Rr