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Transactions on Computational Science VII pp 75–100Cite as

The Solution of Non-linear Diffusion Equation under Stochastic Nonhomogeneity Using Symbolic WHEP and Pickard Algorithms

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Part of the book series: Lecture Notes in Computer Science ((TCOMPUTATSCIE,volume 5890))

Abstract

In this paper, a nonlinear diffusion equation is studied under stochastic nonhomogeneity through homogeneous boundary conditions. The analytical solution for the linear case is obtained using the eigenfunction expansion. The Pickard approximation method is used to introduce a first order approximate solution for the nonlinear case. The WHEP technique is also used to obtain approximate solution under different orders and different corrections. Using Mathematica-5, the solution algorithm is operated through first order approximation. The method of solution is illustrated through case studies and figures.

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Author information

Authors and Affiliations

  1. Faculty of Engineering, Engineering, Mathematics Department, Cairo University, Giza, Egypt

    Magdy A. El-Tawil

  2. Faculty of science, Mathematics Department, King Faisal University, Dammam, Saudi Arabia

    Noha A. Al-Mulla

Authors
  1. Magdy A. El-Tawil
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  2. Noha A. Al-Mulla
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Editors and Affiliations

  1. Department of Computer Science, University of Calgary, 2500 University Drive N.W., T2N 1N4, Calgary, AB, Canada

    Marina L. Gavrilova

  2. Exascala Ltd., Unit 9, 97 Rickman Drive, B15 2AL, Birmingham, UK

    C. J. Kenneth Tan

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El-Tawil, M.A., Al-Mulla, N.A. (2010). The Solution of Non-linear Diffusion Equation under Stochastic Nonhomogeneity Using Symbolic WHEP and Pickard Algorithms. In: Gavrilova, M.L., Tan, C.J.K. (eds) Transactions on Computational Science VII. Lecture Notes in Computer Science, vol 5890. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11389-5_5

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  • DOI: https://doi.org/10.1007/978-3-642-11389-5_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-11388-8

  • Online ISBN: 978-3-642-11389-5

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