Numerical method for solving the fractional evolutionary model of bi-flux diffusion processes

A Finite Difference Method for Solving the Wave Equation with Fractional Damping

“…It should be pointed out that the time discretization technique used in this paper is based on the uniform time mesh, which requires strong regularity assumptions. Recent works [18,25,38,39] have discussed the lack of the smoothness near the initial time of the solution of the time-fractional PDEs. Future study will consider the numerical method in a graded time mesh in order to overcome initial time singularity and provide a theoretical basis for the subsequent numerical scheme.…”

“…Consequently, the study of efficient numerical algorithms for solving the FPDEs plays a critical role in scientific computing and engineering applications. At present, many numerical methods have been developed for solving the FPDEs, such as finite difference methods [18][19][20][21][22][23][24][25], finite element methods [26][27][28][29][30], and spectral methods [31,32].…”