Study of two-dimensional nonlinear coupled time-space fractional order reaction advection diffusion equations using shifted Legendre-Gauss-Lobatto collocation method

IF 1.9 4区工程技术 Q3 MECHANICS

Continuum Mechanics and Thermodynamics Pub Date : 2024-11-23 DOI:10.1007/s00161-024-01338-9

Anjuman, Manish Chopra, Subir Das, Holm Altenbach

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引用次数: 0

Abstract

In this article, the nonlinear coupled two-dimensional space-time fractional order reaction-advection–diffusion equations (2D-STFRADEs) with initial and boundary conditions is solved by using Shifted Legendre-Gauss-Lobatto Collocation method (SLGLCM) with fractional derivative defined in Caputo sense. The SLGLC scheme is used to discretize the coupled nonlinear 2D-STFRADEs into the shifted Legendre polynomial roots to convert it to a system of algebraic equations. The efficiency and efficacy of the scheme are confirmed through error analysis while applying the scheme on two existing problems having exact solutions. The impact of advection and reaction terms on the solution profiles for various space and time fractional order derivatives are shown graphically for different particular cases. A drive has been made to study the convergence of the proposed scheme, which has been applied on the proposed mathematical model.

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使用移位 Legendre-Gauss-Lobatto 配位法研究二维非线性耦合时空分数阶反应平流扩散方程

本文采用移位 Legendre-Gauss-Lobatto Collocation 方法（SLGLCM）求解了具有初始条件和边界条件的非线性耦合二维时空分数阶反应-平流-扩散方程（2D-STFRADEs），并定义了 Caputo 意义上的分数导数。SLGLC 方案用于将耦合非线性 2D-STFRADE 离散化为移位 Legendre 多项式根，从而将其转换为代数方程系统。在对两个已有精确解的问题应用该方案时，通过误差分析证实了该方案的效率和功效。在不同的特殊情况下，平流和反应项对各种空间和时间分数阶导数的解剖面的影响以图形显示。我们还对提议方案的收敛性进行了研究，并将其应用于提议的数学模型。

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

Continuum Mechanics and Thermodynamics 物理-力学

CiteScore

5.30

自引率

15.40%

发文量

审稿时长

>12 weeks

期刊介绍： This interdisciplinary journal provides a forum for presenting new ideas in continuum and quasi-continuum modeling of systems with a large number of degrees of freedom and sufficient complexity to require thermodynamic closure. Major emphasis is placed on papers attempting to bridge the gap between discrete and continuum approaches as well as micro- and macro-scales, by means of homogenization, statistical averaging and other mathematical tools aimed at the judicial elimination of small time and length scales. The journal is particularly interested in contributions focusing on a simultaneous description of complex systems at several disparate scales. Papers presenting and explaining new experimental findings are highly encouraged. The journal welcomes numerical studies aimed at understanding the physical nature of the phenomena. Potential subjects range from boiling and turbulence to plasticity and earthquakes. Studies of fluids and solids with nonlinear and non-local interactions, multiple fields and multi-scale responses, nontrivial dissipative properties and complex dynamics are expected to have a strong presence in the pages of the journal. An incomplete list of featured topics includes: active solids and liquids, nano-scale effects and molecular structure of materials, singularities in fluid and solid mechanics, polymers, elastomers and liquid crystals, rheology, cavitation and fracture, hysteresis and friction, mechanics of solid and liquid phase transformations, composite, porous and granular media, scaling in statics and dynamics, large scale processes and geomechanics, stochastic aspects of mechanics. The journal would also like to attract papers addressing the very foundations of thermodynamics and kinetics of continuum processes. Of special interest are contributions to the emerging areas of biophysics and biomechanics of cells, bones and tissues leading to new continuum and thermodynamical models.