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Special Topics & Reviews in Porous Media: An International Journal

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ISSN Печать: 2151-4798

ISSN Онлайн: 2151-562X

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OPERATIONAL MATRIX METHOD FOR SOLVING NONLINEAR SPACE-TIME FRACTIONAL ORDER REACTION-DIFFUSION EQUATION BASED ON GENOCCHI POLYNOMIAL

Том 11, Выпуск 1, 2020, pp. 33-47
DOI: 10.1615/SpecialTopicsRevPorousMedia.2020030750
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Краткое описание

An operational matrix method with Genocchi polynomials is derived to solve a space-time fractional order nonlinear reaction-diffusion equation with forced term. Applying a collocation method and using the operational matrix, a fractional order nonlinear partial differential equation is reduced to a system of algebraic equations, which can be solved by using Newton iteration. The salient features of the article are the pictorial presentations of the numerical solution of the concerned equation for different particular cases to show the effect of reaction term on the solution profile and also the change of its behavior when the system goes from standard order to fractional order. The accuracy of our proposed method is validated through the error analysis between the obtained numerical results and the analytical results of two existing standard order models.

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ЦИТИРОВАНО В
  1. Zhao Jie, Fang Zhichao, Li Hong, Liu Yang, Finite volume element method with the WSGD formula for nonlinear fractional mobile/immobile transport equations, Advances in Difference Equations, 2020, 1, 2020. Crossref

  2. Kumar Sachin, Ahmad Bashir, A new numerical study of space–time fractional advection–reaction–diffusion equation with Rabotnov fractional‐exponential kernel, Numerical Methods for Partial Differential Equations, 2020. Crossref

  3. Kumar Sachin, Numerical solution of fuzzy fractional diffusion equation by Chebyshev spectral method, Numerical Methods for Partial Differential Equations, 2020. Crossref

  4. Kumar Sachin, Cao Jinde, Li Xiaodi, A Numerical Method for Time-Fractional Reaction-Diffusion and Integro Reaction-Diffusion Equation Based on Quasi-Wavelet, Complexity, 2020, 2020. Crossref

  5. Kashif Mohd., Dwivedi Kushal Dhar, Som T., Numerical solution of coupled type Fractional order Burgers’ equation using Finite Difference and Fibonacci Collocation Method, Chinese Journal of Physics, 77, 2022. Crossref

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