Abstract
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.
Highlights
Partial differential equations (PDEs) with time delay play an important role in the mathematical modeling of complex phenomena and processes whose states depend on a given moment in time and on one or more previous moments
Because the drug must be introduced into the bloodstream for it to take effect, the preceding scenario can be interpreted as a delay problem
Á ðt − sÞ1−νds, ν ∈ ð1, 2Þ: A novel interpolating element-free Galerkin approach to approximate the solution of the two-dimensional elastoplasticity problems was constructed in [15] using the interpolating moving least squares scheme for obtaining the shape function
Summary
Partial differential equations (PDEs) with time delay play an important role in the mathematical modeling of complex phenomena and processes whose states depend on a given moment in time and on one or more previous moments. A novel interpolating element-free Galerkin approach to approximate the solution of the two-dimensional elastoplasticity problems was constructed in [15] using the interpolating moving least squares scheme for obtaining the shape function. The interpolating moving least squares approach using a nonsingular weight function is employed in [17] to approximate the solution of the problem of inhomogeneous swelling of polymer gels, and the penalty scheme is used to enforce the displacement boundary condition; an improved element-free Galerkin approach was constructed. For the numerical solution of generalised Oseen problems, a novel variational multiscale interpolating element-free Galerkin scheme was developed in [33] based on moving Kriging interpolation for obtaining shape functions using the Kronecker delta function.
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