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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Chebyshev polynomial approximations for some hyper
geometric systems\n - Rappoport\, J (Russian Acade
my of Sciences)
DTSTART;TZID=Europe/London:20090703T120000
DTEND;TZID=Europe/London:20090703T123000
UID:TALK18969AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/18969
DESCRIPTION:The hypergeometric type differential equations of
the second order with polynomial coefficients and
their systems are considered. The realization of t
he Lanczos Tau method with minimal residue is prop
osed for the approximate solution of the second or
der differential equations with polynomial coeffic
ients. The scheme of Tau method is extended for th
e systems of hypergeometric type differential equa
tions. A Tau method computational scheme is applie
d to the approximate solution of a system of diffe
rential equations related to the differential equa
tion of hypergeometric type. The case of the discr
ete systems may be considered also. Various vector
perturbations are discussed. Our choice of the pe
rturbation term is a shifted Chebyshev polynomial
with a special form of selected transition and nor
malization. The minimality conditions for the pert
urbation term are found for one equation. They are
sufficiently simple for the verification in a num
ber of important cases. Several approaches for the
approximation of kernels of Kontorovich-Lebedev i
ntegral transforms--modified Bessel functions of t
he second kind with pure imaginary order and with
complex order are elaborated. The codes of the eva
luation are constructed and tables of the modified
Bessel functions are published. The advantages of
discussed algorithms in accuracy and timing are s
hown. The effective applications for the solution
of some mixed boundary value problems in wedge dom
ains are given. \n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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