ON THE ASYMPTOTIC SOLUTIONS OF A DIFFERENTIAL-EQUATION WITH MULTIPLE SINGULAR POINTS

[摘要] A singularly perturbed model problem with multiple distinct regular points is studied. The uniform approximation of Wazwaz and Hanson (1986) is effectively extended to many singular points, thus establishing a generalized version of that theorem where the classic inner and outer expansions are not employed. A leading order general asymptotic solution is correctly represented by a set of matched exponential asymptotic expansions, where each approximation contains dominant and recessive terms. The resonance criteria due to the influence of multiple singular points are discussed. For an even number of singular points, the eigenvalues were found to be positive with a minimal eigenvalue. However, negative eigenvalues with a maximal eigenvalue arise for an odd number of singular points. The maximal and the minimal eigenvalue may not be unique and each is O(1).

[发布日期] 1991-02-10

[关键词] SINGULAR POINTS;SINGULAR PERTURBATIONS;MATCHED ASYMPTOTIC EXPANSIONS;EXPONENTIAL PRECISION ASYMPTOTICS;SINGULAR POINT RESONANCE