An effective linear scheme to solve nonlinear degenerate parabolic differential equations

In this paper, we consider the approximate solution of the following problem. Given ω RN (1 N 3), find u(x, t) such that ∂tb(u)−Δu+Pe u=0, in Q ω×(0,T), u=0, on ∑ ∂ω×(0,T), u(x,0)=u0(x), x ω, where the function b(s) is a monotonically increasing function satisfying 0 b′ ∞ To solve this problem, we introduce a new nonstandard time discretization scheme. We prove stability and convergence results.