Bernoulli Collocation Method for Solving Time‐Fractional Diffusion Equation Arising in Physics

ABSTRACT This research presents an effective spectral collocation scheme based on orthogonalized Bernoulli polynomials for solving the time‐fractional diffusion equation (TFDE). To provide a numerical method, we consider the Bernoulli polynomials and estimate the derivatives as well as the Caputo fractional derivative by operational matrices. By collocating the discretized equations, we obtain a system of algebraic equations. By solving this system, we obtain the approximate solution. The advantages of the suggested method are its low computational cost and exponential convergence. Also, the convergence analysis of the presented method is discussed. Finally, we present several test problems to demonstrate the capability of the proposed method. The obtained results are compared with the existing methods in the literature.