Interpolating Stabilized Element Free Galerkin Method for Neutral Delay Fractional Damped Diffusion-Wave Equation

A numerical solution for neutral delay fractional order partial differential equations involving the Caputo fractional derivative is constructed. In line with this goal, the drift term and the time Caputo fractional derivative are discretized by a finite difference approximation. The energy method is used to investigate the rate of convergence and unconditional stability of the temporal discretization. The interpolation of moving Kriging technique is then used to approximate the space derivative, yielding a meshless numerical formulation. We conclude with some numerical experiments that validate the theoretical findings.

Automated summary

This research presents a numerical solution for neutral delay fractional order partial differential equations involving the Caputo fractional derivative through finite difference approximation. The energy method is utilized to investigate the convergence rate and stability of temporal discretization. Additionally, the interpolation of moving Kriging technique is applied for approximating the space derivative, leading to a meshless numerical formulation. Finally, theoretical findings are confirmed through numerical experiments.