TY - JOUR
T1 - On a Two-Point Boundary-Value Problem with Spurious Solutions
AU - Ou, C. H.
AU - Wong, R.
PY - 2003/11
Y1 - 2003/11
N2 - The Carrier-Pearson equation εü + u2 = 1 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.
AB - The Carrier-Pearson equation εü + u2 = 1 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.
UR - http://www.scopus.com/inward/record.url?scp=0142215380&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-0142215380&origin=recordpage
U2 - 10.1111/1467-9590.t01-1-00039
DO - 10.1111/1467-9590.t01-1-00039
M3 - RGC 21 - Publication in refereed journal
SN - 0022-2526
VL - 111
SP - 377
EP - 408
JO - Studies in Applied Mathematics
JF - Studies in Applied Mathematics
IS - 4
ER -