Collocation method with Lagrange polynomials for variable-order time-fractional advection-diffusion problems

In this study, we proposed a numerical technique to solve a class of variable-order time-fractional advection-diffusion equations (VOTFADEs) by applying an operational matrix of differentiation based on fractional-order Lagrange polynomials (FOLPs). The variable-order fractional derivative is assumed to be Caputo's derivative. Using the operational matrix and collocation method, the advection-diffusion equation can be reduced to an algebraic system of equations that can be solved using Newton's iterative method. Error analysis also has been carried out for the proposed method. The current approach is simple to use and computer oriented and provides highly accurate approximate solutions. The effectiveness and accuracy of the proposed method are demonstrated using a few numerical examples.

Automated summary

In this study, a numerical technique using fractional-order Lagrange polynomials and Newton's iterative method is proposed to solve variable-order time-fractional advection-diffusion equations. The method is simple to use and provides highly accurate approximate solutions.