TY - JOUR
T1 - Analytical and computational methods for a class of nonlinear singular integral equations
AU - Allaei, Sonia Seyed
AU - Diogo, Teresa
AU - Rebelo, Magda
N1 - Sem PDF.
CT-Fundacao para a Ciencia e a Tecnologia (Pest-OE/MAT/UI0822/2014; PTDC/MAT/101867/2008)
FCT (UID/MAT/00297/2013)
PY - 2017/4
Y1 - 2017/4
N2 - We consider a class of nonlinear singular Hammerstein Volterra integral equations. In general, these equations will have kernels containing both an end point and an Abel-type singularity, with exact solutions being typically nonsmooth. Under certain conditions, a uniformly convergent iterative solution is obtained on a small interval near the origin. In this work, two product integration methods are proposed and analyzed where the integral over a small initial interval is calculated analytically, allowing the optimal convergence rates to be achieved. This is illustrated by some numerical examples.
AB - We consider a class of nonlinear singular Hammerstein Volterra integral equations. In general, these equations will have kernels containing both an end point and an Abel-type singularity, with exact solutions being typically nonsmooth. Under certain conditions, a uniformly convergent iterative solution is obtained on a small interval near the origin. In this work, two product integration methods are proposed and analyzed where the integral over a small initial interval is calculated analytically, allowing the optimal convergence rates to be achieved. This is illustrated by some numerical examples.
KW - Hammerstein equations
KW - Iterative solution
KW - Nonlinear Volterra integral equation
KW - Product integration method
KW - Weakly singular kernel
UR - http://www.scopus.com/inward/record.url?scp=84997703680&partnerID=8YFLogxK
U2 - 10.1016/j.apnum.2016.06.001
DO - 10.1016/j.apnum.2016.06.001
M3 - Article
AN - SCOPUS:84997703680
SN - 0168-9274
VL - 114
SP - 2
EP - 17
JO - Applied Numerical Mathematics
JF - Applied Numerical Mathematics
IS - SI
ER -