Numerical solution of fractional advection-diffusion equation with a nonlinear source term

作者：Parvizi M; Eslahchi M R^*; Dehghan Mehdi

来源：Numerical Algorithms, 2015, 68(3): 601-629.

DOI：10.1007/s11075-014-9863-7

• Fractional advection-diffusion equation
• Riemann-Liouville derivative
• Jacobi polynomials
• Operational matrix
• Collocation method
• Stability analysis and convergence

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 < sigma a parts per thousand currency sign 1 and 1 < mu a parts per thousand currency sign 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.

• 出版日期2015-3