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On a Two‐Point Boundary‐Value Problem with Spurious Solutions
Author(s) -
Ou C. H.,
Wong R.
Publication year - 2003
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/1467-9590.t01-1-00039
Subject(s) - spurious relationship , mathematics , boundary value problem , mathematical analysis , point (geometry) , boundary (topology) , boundary values , statistics , geometry
The Carrier–Pearson equation with boundary conditions u (−1) = u (1) = 0 is studied from a rigorous point of view. Known solutions obtained from the method of matched asymptotics are shown to approximate true solutions within an exponentially small error estimate. The so‐called spurious solutions turn out to be approximations of true solutions, when the locations of their “spikes” are properly assigned. An estimate is also given for the maximum number of spikes that these solutions can have.