Treffer: Symbolic Generation of Adomian Polynomials for Different Nonlinearities by Python.

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, integrodifferential, 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. [ABSTRACT FROM AUTHOR]

المقال يناقش تطوير كود بلغة بايثون للتوليد الرمزي لحدود أدوميان، والتي تعتبر حاسمة لتطبيق طريقة تحليل أدوميان (ADM) على المعادلات الوظيفية غير الخطية. يبرز المقال استخدام مكتبة SymPy لتعزيز كفاءة حساب هذه الحدود مقارنةً بالطرق التقليدية التي تستخدم بيئات برمجة أكثر تعقيدًا مثل Maple أو MATLAB. يقدم المؤلفون أمثلة توضح فعالية الكود ويستعرضون تطبيقاته المحتملة في حل المعادلات غير الخطية في هندسة الكيمياء. بالإضافة إلى ذلك، يتضمن المقال معلومات حقوق النشر ورابطًا لتحميل السكربت الكامل بلغة بايثون. [Extracted from the article]

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