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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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.
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Variable-Order Derivative, Nonlinear Galilei Invariant Advection-Diffusion Equation, Collocation Method, Legendre Polynomials
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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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Advances in Difference Equations