Numerical solution of one- and two-dimensional time-fractional Burgers equation via Lucas polynomials coupled with Finite difference method

In this article, a numerical technique based on polynomials is proposed for the solution of one and two-dimensional time-fractional Burgers equation. First, the given problem is reduced to time discrete form using θ-weighted scheme. Then, with the help of Lucas and Fibonacci polynomials the given PDEs transformed to system of algebraic equations which is easy to solve. The proposed algorithm is validated by solving some numerical examples. Despite this, convergence analysis of the scheme is briefly discussed and verified numerically. The main objective of this paper is to show that polynomial based method is convenient for 1D and 2D nonlinear time-fractional partial differential equations (TFPDEs). Efficiency and performance of the proposed technique are examined by calculating L₂ and L_∞ error norms. Obtained accurate results confirm applicability and efficiency of the method.