An Implicit Numerical Method for the Riemann–Liouville Distributed-Order Space Fractional Diffusion Equation

This paper investigates a two-dimensional Riemann–Liouville distributed-order space fractional diffusion equation (RLDO-SFDE). However, many challenges exist in deriving analytical solutions for dynamic systems. Efficient and reliable methods need to be explored solving the RLDO-SFDE numerically. We develop an alternating direction implicit scheme prove that numerical method is unconditionally stable convergent with accuracy of O(σ2+ρ2+τ+hx+hy). After employing extrapolated technique, convergence order improved second time space. Furthermore, fast algorithm constructed reduce computational costs. Two examples are presented verify effectiveness methods. study may provide more possibilities simulating complexities by calculus.