The behavior of a finite difference approximation to a singular initial boundary value problem

Abstract

We develop difference approximations to a singular parabolic initial-boundary value problem and its corresponding steady-state problem. A critical value for the existence of nonnegative solutions to the discrete steady state system is established. Convergence of the computed critical values is obtained. The long time behavior for the approximated solution of the parabolic problem is investigated. It is shown that the behavior of the discrete system is consistent with that of the continuous one

Keywords:

• Singular initial boundary value problem
• difference approximation
• convergence
• long time behavior

AMS:

• 35K57
• 65M06
• 65M12