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.
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Parvizi, M., Eslahchi, M.R. & Dehghan, M. Numerical solution of fractional advection-diffusion equation with a nonlinear source term. Numer Algor 68, 601–629 (2015). https://doi.org/10.1007/s11075-014-9863-7
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DOI: https://doi.org/10.1007/s11075-014-9863-7
Keywords
- Fractional advection-diffusion equation
- Riemann-Liouville derivative
- Jacobi polynomials
- Operational matrix
- Collocation method
- Stability analysis and convergence.