Zhi-zhong Sun

TL;DR: In this paper, a fully discrete difference scheme is derived for a diffusion-wave system by introducing two new variables to transform the original equation into a low order system of equations. And the solvability, stability and L∞ convergence are proved by the energy method.

TL;DR: The comparison with the corresponding results of finite difference methods by the L1 formula demonstrates that the new L1-2 formula is much more effective and more accurate than the L2 formula when solving time-fractional differential equations numerically.

TL;DR: The stability and convergence of the finite difference scheme in maximum norm are proved using the energy method, where a new inner product is introduced for the theoretical analysis.

TL;DR: It is proved that the difference scheme is uniquely solvable, stable, and convergent with order $O(\tau^2+h^4)$, where $\tau$ is the time step size and $h=\max\{h_1,h_2\}$ are space grid sizes in the x and y direction.

TL;DR: The finite difference approximation of Caputo derivative on non-uniform meshes is investigated and a semi-discrete scheme is obtained and the unconditional stability and H^1 norm convergence are proved.