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Improved High Order Methods Using Boundary Layer Detection for a Singular Perturbation Problem

from Chang [1], O’Malley [2] and Miller [3]. Using the boundary layer detection theorem in Zhang [4], an exponential boundary layer of width proportional the singular perturbation parameter can be found to the left boundary. Because of the presence of the boundary layer, the numerical methods from Keller [5] will have to be adjusted accordingly. Choudhury [6] and Ilicasu [7] solved the problem using nonstandard high order methods on a uniform mesh. With the theory of weak formulation in Lax [8], Zhang [9] proposed test functions fitting the exponential boundary layer to solve the singular perturbation. In this paper, the singular perturbation problem is solved with improved high order methods based on the boundary layer detection theorem. Furthermore, a sixth order method is developed and verified numerically. An improvement on the 4 order method Let 1 ω ε = where ε is the singular perturbation parameter in the problem (1). Then we rewrite the second order deriv-