Operational Matrix Approach for Solving the Variable-Order Nonlinear Galilei Invariant Advection-Diffusion Equation
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Date
2018
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Springer international Publishing Ag
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GOLD
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Abstract
In this paper, we investigate numerical solution of the variable-order fractional Galilei advection-diffusion equation with a nonlinear source term. The suggested method is based on the shifted Legendre collocation procedure and a matrix form representation of variable-order Caputo fractional derivative. The main advantage of the proposed method is investigating a global approximation for the spatial and temporal discretizations. This method reduces the problem to a system of algebraic equations, which is easier to solve. The validity and effectiveness of the method are illustrated by an easy-to-follow example.
Description
Zaky, Mahmoud/0000-0002-3376-7238
ORCID
Keywords
Variable-Order Derivative, Nonlinear Galilei Invariant Advection-Diffusion Equation, Collocation Method, Legendre Polynomials, Composite material, Matrix (chemical analysis), Mathematical analysis, Quantum mechanics, Convergence Analysis of Iterative Methods for Nonlinear Equations, Differential equation, QA1-939, FOS: Mathematics, Nonlinear Galilei invariant advection–diffusion equation, Variable (mathematics), Collocation method, Anomalous Diffusion Modeling and Analysis, Numerical Analysis, Time-Fractional Diffusion Equation, Physics, Statistical and Nonlinear Physics, Partial differential equation, Invariant (physics), Applied mathematics, Materials science, Physics and Astronomy, Modeling and Simulation, Mathematical physics, Physical Sciences, Nonlinear system, Advection, Legendre polynomials, Thermodynamics, Variable-order derivative, Mathematics, Ordinary differential equation, Rogue Waves in Nonlinear Systems, Algebraic equation, Fractional derivatives and integrals, Finite difference methods for initial value and initial-boundary value problems involving PDEs, nonlinear Galilei invariant advection-diffusion equation, variable-order derivative, Fractional partial differential equations, collocation method, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
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Fields of Science
01 natural sciences, 0103 physical sciences, 0101 mathematics
Citation
Zaky, M. A...et al. (2018). "Operational matrix approach for solving the variable-order nonlinear Galilei invariant advection-diffusion equation", Advances in Difference Equations.
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Q1
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OpenCitations Citation Count
24
Source
Advances in Difference Equations
Volume
2018
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CrossRef : 20
Scopus : 28
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28
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20
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2
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