Numerical solution of fractional advection-diffusion equation with a nonlinear source term
Numerical Algorithms, 2015•Springer
In this paper we use the Jacobi collocation method for solving a special kind of the fractional
advection-diffusion equation with a nonlinear source term. This equation is the classical
advection-diffusion equation in which the space derivatives are replaced by the Riemann-
Liouville derivatives of order 0< σ≤ 1 and 1< μ≤ 2. Also the stability and convergence of the
presented method are shown for this equation. Finally some numerical examples are solved
using the presented method.
advection-diffusion equation with a nonlinear source term. This equation is the classical
advection-diffusion equation in which the space derivatives are replaced by the Riemann-
Liouville derivatives of order 0< σ≤ 1 and 1< μ≤ 2. Also the stability and convergence of the
presented method are shown for this equation. Finally some numerical examples are solved
using the presented method.
Abstract
In this paper we use the Jacobi collocation method for solving a special kind of the fractional advection-diffusion equation with a nonlinear source term. This equation is the classical advection-diffusion equation in which the space derivatives are replaced by the Riemann-Liouville derivatives of order 0 < σ ≤ 1 and 1 < μ ≤ 2. Also the stability and convergence of the presented method are shown for this equation. Finally some numerical examples are solved using the presented method.
Springer
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