A novel numerical manner for non-linear coupled variable order reaction-diffusion equation

IF 1.1 4区 工程技术 Q4 THERMODYNAMICS
Mohd. Kashif, P. Pandey, H. Jafari
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引用次数: 0

Abstract

In this work, an efficient variable order Bernstein collocation technique, which is based on Bernstein polynomials, is applied to a non-linear coupled system of variable order reaction-diffusion equations with given initial and boundary conditions. The operational matrix of Bernstein polynomials is derived for variable order derivatives w.r.t. time and space. The Bernstein operational matrix and collocation technique are applied to the concerned non-linear physical model to achieve a system of non-linear algebraic equations, which are further solved by using Newton method. A few examples are presented to demonstrate the accuracy and stability of the scheme by comparing L2 and L? norm errors between the obtained numerical solutions and existing solutions. The important feature of this article is the graphical exhibitions of the effects of variable order derivatives on the solutions of the considered non-linear coupled reaction-diffusion equation for different particular cases.
非线性耦合变阶反应扩散方程的一种新的数值解法
本文将基于Bernstein多项式的高效变阶Bernstein配置技术应用于具有给定初始条件和边界条件的变阶反应扩散方程的非线性耦合系统。对变阶导数在时间和空间上w.r.t.,导出了Bernstein多项式的运算矩阵。将Bernstein操作矩阵和配置技术应用于相关的非线性物理模型,得到一个非线性代数方程组,并用牛顿法进一步求解。通过比较L2和L?得到的数值解与现有解之间的范数误差。本文的重要特点是用图形展示了不同特殊情况下变阶导数对所考虑的非线性耦合反应扩散方程解的影响。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Thermal Science
Thermal Science 工程技术-热力学
CiteScore
2.70
自引率
29.40%
发文量
399
审稿时长
5 months
期刊介绍: The main aims of Thermal Science to publish papers giving results of the fundamental and applied research in different, but closely connected fields: fluid mechanics (mainly turbulent flows), heat transfer, mass transfer, combustion and chemical processes in single, and specifically in multi-phase and multi-component flows in high-temperature chemically reacting flows processes present in thermal engineering, energy generating or consuming equipment, process and chemical engineering equipment and devices, ecological engineering, The important characteristic of the journal is the orientation to the fundamental results of the investigations of different physical and chemical processes, always jointly present in real conditions, and their mutual influence. To publish papers written by experts from different fields: mechanical engineering, chemical engineering, fluid dynamics, thermodynamics and related fields. To inform international scientific community about the recent, and most prominent fundamental results achieved in the South-East European region, and particularly in Serbia, and - vice versa - to inform the scientific community from South-East European Region about recent fundamental and applied scientific achievements in developed countries, serving as a basis for technology development. To achieve international standards of the published papers, by the engagement of experts from different countries in the International Advisory board.
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