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 $0<\alpha\leq1$, 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.