An effective linear scheme to solve nonlinear degenerate parabolic differential equations

Abstract

In this paper, we consider the approximate solution of the following problem. Given ω⊂ R N (1 ⪯ N ⪯ 3), find u(x, t) such that ∂ tb(u)−Δu+P e▽u=0, in Qω×(0,T) , u=0, on ∑∂ω×(0,T) , u(x,0)=u 0(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.