Symbolic Generation of Adomian Polynomials for Different Nonlinearities by Python

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Noorimohammad Mohsen; Houshmand Asadollah; Fatoorehchi Hooman

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Journal Paper

Paper Information

Journal: Journal of Chemical and Petroleum Engineering Year:2024 | Volume:58 | Issue:1 Page(s): 103-114

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Information Journal Paper

Title

Symbolic Generation of Adomian Polynomials for Different Nonlinearities by Python

Author(s)

Noorimohammad Mohsen | Houshmand Asadollah | Fatoorehchi Hooman | Issue Writer Certificate

Keywords

Adomian Decomposition MethodQ4

Adomian PolynomialsQ4

Differential equationsQ4

Nonlinear equationsQ4

PythonQ4

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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