TY - JOUR
T1 - Modified Galerkin Method for Derivative Dependent Fredholm–Hammerstein Integral Equations of Second Kind
AU - Kant , Kapil
AU - Das , Payel
AU - Nelakanti , Gnaneshwar
AU - Kumar , Ratish
JO - Advances in Applied Mathematics and Mechanics
VL - 4
SP - 905
EP - 926
PY - 2024
DA - 2024/05
SN - 16
DO - http://doi.org/10.4208/aamm.OA-2022-0277
UR - https://global-sci.org/intro/article_detail/aamm/23116.html
KW - Fredholm integral equations, Green’s kernel, modified Galerkin method, piecewise polynomial, superconvergence rates.
AB - <p style="text-align: justify;">In this paper, we consider modified Galerkin and iterated modified Galerkin
methods for solving a class of two point boundary value problems. The methods are
applied after constructing the equivalent derivative dependent Fredholm-Hammerstein
integral equations to the boundary value problem. Existence and convergence of the
approximate solutions to the actual solution is discussed and the rates of convergence
are obtained. Superconvergence results for the approximate and iterated approximate
solutions of piecewise polynomial based modified Galerkin method in infinity norm
are given. We have also established that iterated modified Galerkin approximation
improves over the modified Galerkin solution. Numerical examples are presented to
illustrate the theoretical results.</p>