# An approximate solution based on Jacobi polynomials for time-fractional convection–diffusion equation

*M. Behroozifar* and
*A. Sazmand*

*Applied Mathematics and Computation*, 2017, vol. 296, issue C, 1-17

**Abstract:**
In this article, we present a numerical method to numerically solve a time-fractional convection–diffusion equation. Our method is based on the operational matrices of shifted Jacobi polynomials. At first, problem is converted to a homogeneous problem by interpolation and afterward an integro-differential equation is yielded. Then we approximate the known and unknown functions with the help of shifted Jacobi functions. A system of nonlinear algebraic equations is obtained. Finally, the unknown coefficients are determined by MathematicaTM. We implemented the proposed method for several examples that they indicate the high accuracy method. It should be noted that this method is generalizable to some appropriate problems.

**Keywords:** Time-fractional convection–diffusion equation; Caputo fractional derivative; Jacobi polynomials (search for similar items in EconPapers)

**Date:** 2017

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**Persistent link:** https://EconPapers.repec.org/RePEc:eee:apmaco:v:296:y:2017:i:c:p:1-17

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