On a recursive approximation of singularly perturbed parabolic equations

[摘要] The asymptotic analysis of IBVPs for the singularly perturbed parabolic PDE partial derivative (t)u + partial derivative (x)u = epsilon partial derivative (xx)u in the limit epsilon --> 0 motivates investigations of certain recursively defined approximative series (ping-pong expansions). The recursion formulae rely on operators assigning to a boundary condition at the left or the right boundary a solution of the parabolic PDE. Sufficient conditions for uniform convergence of ping-pong expansions are derived and a detailed analysis for the model problem partial derivative (t)u + partial derivative (x)u = epsilon partial derivative (xx)u is given. (C) 2000 Academic Press.

[发布日期] 2000-10-01