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 -