The convergence of high-accuracy three-point compact computational method for structural derivative anomalous diffusion–advection model

A computational method based on compact discretization for solving the nonlinear anomalous diffusion–advection model is proposed via the structural derivative. The structural derivative model is a promising technique for characterizing complex and gradual creep phenomena. The structural function considered here is the algebraic function, which can be used to represent anomalous diffusion at different rates depending on the choice of the fractal parameter value. The operational iteration matrices take the tri-diagonal form and are easily solved for the approximate solutions. A strongly connected graph of Jacobian matrices is investigated to establish the discrete scheme's convergence. Numerical simulations are conducted to demonstrate the accuracy, efficiency, and simplicity of the compact computational method. According to the findings, the suggested model outperforms the conventional approach in terms of accuracy and usability.