Open AccessBOOLE COLLOCATION METHOD BASED ON RESIDUAL CORRECTION FOR SOLVING LINEAR FREDHOLM INTEGRO-DIFFERENTIAL EQUATION
Author(s) -
Hale Gül Dağ,
Kübra Erdem Biçer
Publication year - 2020
Publication title -
journal of science and arts
Language(s) - English
Resource type - Journals
eISSN - 2068-3049
pISSN - 1844-9581
DOI - 10.46939/j.sci.arts-20.3-a09
Subject(s) - fredholm integral equation , mathematics , collocation (remote sensing) , residual , polynomial , method of mean weighted residuals , differential equation , collocation method , matrix (chemical analysis) , fredholm theory , orthogonal collocation , integro differential equation , mathematical analysis , integral equation , finite element method , ordinary differential equation , first order partial differential equation , algorithm , computer science , physics , materials science , machine learning , galerkin method , composite material , thermodynamics
In this study, a Boole polynomial based method is presented for solving the linear Fredholm integro-differential equation approximately. In this method, the given problem is reduced to a matrix equation. The solution of the obtained matrix equation is found by using Boole polynomial, its derivatives and collocation points. This solution is obtained as the truncated Boole series which are defined in the interval [a,b]. In order to demonstrate the validity and applicability of the method, numerical examples are included. Also, the error analysis related with residual function is performed and the found approximate solutions are calculated.