A novel finite difference scheme for numerical solution of fractional order population growth model

Abstract

In this paper, we propose a new scheme based on the implicit finite difference method for solving the fractional population growth model (FPGM). We use the well-known L1 finite difference method to approximate the Caputo fractional derivative of order 0 < α ≤ 1, and the linear interpolation to approximate the integral part. We provide a study on the stability and convergence of the scheme. We present the numerical solution of the proposed method and compare it with three other methods to demonstrate its validity and efficiency.