Symbolic Generation of Adomian Polynomials for Different Nonlinearities by Python

Document Type : Research Paper

Authors

1 School of Chemical Engineering, College of Engineering, University of Tehran, P.O. Box 11365-4563, Tehran, Iran

2 Chemical Engineering, University of Tehran, Tehran, Iran

Abstract

The Adomian decomposition method (ADM) is a powerful mathematical technique to find closed-form solutions to nonlinear functional equations including ODEs, PDEs, differential-difference, integral, integro-differential, algebraic, and transcendental equations or systems of such equations. It features a particular infinite series for the representation of nonlinear terms of the equation under study, referred to as the Adomian polynomials. Nevertheless, the computation of such polynomials manually, devoid of any assistance from computational resources, can often be a laborious and protracted endeavor. In this paper, an innovative Python code is proposed, which exploits the SymPy library to perform the involved symbolic calculus operations to generate the Adomian polynomials of any given nonlinear expressions. The use of the code would substantially facilitate the implementation of the ADM to the equations arising in various branches of science and engineering. A number of nonlinear expressions are decomposed to their relevant Adomian polynomials for the sake of demonstration.

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Journal of Chemical and Petroleum Engineering

Articles in Press, Accepted Manuscript
Available Online from 14 January 2024

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History

  • Receive Date: 09 November 2023
  • Revise Date: 11 January 2024
  • Accept Date: 13 January 2024

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