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Applications of Adomian Decomposition Method to certain Partial Differential Equations

El-Houssieny, Mohamed E
http://orcid.org/0000-0002-9627-4828
http://rave.ohiolink.edu/etdc/view?acc_num=toledo1628175365385811

Abstract Details

2021, Master of Arts, University of Toledo, Mathematics.
Adomian decomposition method (ADM) was introduced and developed by G. Adomian from the 1970s to the 1990s. The solution procedure of this method is an effective approach to broad classes of linear, non-linear, ordinary, or partial differential equations. This method allows us to handle both initial-value and boundary-value problems with important applications in various fields of applied mathematics, engineering, physics, and biology. Recently a great deal of interest has been focused on the application of ADM to solve a wide variety of stochastic problems. A unique feature of this method is, it deals directly with the nonlinear problem avoiding any linearization or discretization. This is a semi-analytic method and assumes that the solution is decomposed into a rapidly convergent series and the nonlinear term as a series of Adomian Polynomials. This result in the reduction of any differential equation into a set of recursive relation for the Adomian solution series. In this thesis, we first present the methodology and then apply the solution procedure to advection, diffusion, Fisher's, Korteweg-de Vries, Korteweg-de Vries-Burgers, and shallow water equations. The results are compared to either exact or result obtained by different methods.
Vani Cheruvu (Committee Chair)
Alimjon Eshmatov (Committee Member)
Geoffrey Martin (Committee Member)
86 p.
Mathematics
Adomian decomposition method, Korteweg de Vries equation equation, Korteweg-de Vries-Burgers equation, Fisher's equation.

Recommended Citations

Citations

  • El-Houssieny, M. E. (2021). Applications of Adomian Decomposition Method to certain Partial Differential Equations [Master's thesis, University of Toledo]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1628175365385811

    APA Style (7th edition)

  • El-Houssieny, Mohamed. Applications of Adomian Decomposition Method to certain Partial Differential Equations. 2021. University of Toledo, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=toledo1628175365385811.

    MLA Style (8th edition)

  • El-Houssieny, Mohamed. "Applications of Adomian Decomposition Method to certain Partial Differential Equations." Master's thesis, University of Toledo, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1628175365385811

    Chicago Manual of Style (17th edition)

toledo1628175365385811
182
© 2021, some rights reserved.Creative Commons License Applications of Adomian Decomposition Method to certain Partial Differential Equations by Mohamed E El-Houssieny is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Based on a work at etd.ohiolink.edu.
This open access ETD is published by University of Toledo and OhioLINK.