학술논문
Numerical solution of a singularly perturbed Fredholm integro differential equation with Robin boundary condition.
Document Type
Journal
Author
Durmaz, Muhammet Enes (TR-KIRK-IT) AMS Author Profile; Amiraliyev, Gabil M. (TR-EBYUAS-M) AMS Author Profile; Kudu, Mustafa (TR-EBYUAS-M) AMS Author Profile
Source
Subject
45 Integral equations -- 45J Integro-ordinary differential equations
45J05Integro-ordinary differential equations
65Numerical analysis -- 65L Ordinary differential equations
65L12Finite difference methods
65L20Stability and convergence of numerical methods
65Numerical analysis -- 65R Integral equations, integral transforms
65R20Integral equations
45J05
65
65L12
65L20
65
65R20
Language
English
Abstract
In this paper the authors consider equations of the form $$ \int_0^l K(x,s)u(s)ds=f(x),\quad x \in (0,l), $$ with boundary conditions $$ -\sqrt{\varepsilon}u'(0)+\beta u(0)=A,\quad u(l)=B, $$ where $A$ and $B$ are constants. \par Interpolation quadrature formulas are constructed. Difference schemes introduced according to the Shishkin scheme are used. The convergence of the method is proved and error estimates are obtained.