Smoothing Properties of Implicit Finite Difference Methods for a Diffusion Equation in Maximum Norm
Smoothing Properties of Implicit Finite Difference Methods for a Diffusion Equation in Maximum Norm
We prove a regularity property of finite difference schemes for the heat or diffusion equation $u_t = \Delta u$ in maximum norm with large time steps. For a class of time discretizations including L-stable single-step methods and the second-order backward difference formula, with the usual second-order Laplacian, we show that …