On a Recursive Approximation of Singularly Perturbed Parabolic Equations

The asymptotic analysis of IBVPs for the singularly perturbed parabolic PDE tu xu x x u in the limit 0 motivates investigations of certain recursively defined approximative seriesŽ‘‘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 tu xu x x u is given.