| Our goal is to design large time step numerical schemes for a class of Partial Differential Equations. We propose a preconditioning approximation model ∂tuepsilon = o, L(epsilon,D)o = N for PDEs of the form ∂tu = L( u) + N(u), u(0, x) = u(x), where L is a linear operator and N is a nonlinear operator. While applying to linear equations, L can be chosen based on linear stability analysis. Nonlinear problem has to rely on certain intrinsic energy principle. In this paper we will give stability analysis for different types of linear equations and discrete energy analysis for some nonlinear equations. Also numerical examples together with some error analysis for both linear and nonlinear equations will be exhibited to illustrate the computational efficiency of the method... |
