Solving the time-fractional diffusion equation via Sinc-Haar collocation method

- Expanding the approximation with the elements of Sinc and Haar functions.
- An efficient algorithm with exponential convergence rate.
- Computational speed is high due to using the Haar operational matrices.
- To improve the accuracy by increasing the number of collocation points.

The present study investigates the Sinc-Haar collocation method for the solution of the time-fractional diffusion equation. The advantages of this technique are that not only the convergence rate of Sinc approximation is exponential but the computational speed also is high due to the use of the Haar operational matrices. This technique is used to convert the problem to the solution of linear algebraic equations via expanding the required approximation based on the elements of Sinc functions in space and Haar functions in time with unknown coefficients. The effectiveness of the proposed method is examined by comparing the numerical results with the exact solutions.