Boole Collocation Method Based on Residual Correction for Solving Linear Fredholm Integro-Differential Equation

Abstract

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.

An efficient numerical method for a singularly perturbed Fredholm integro-differential equation with integral boundary condition

“…Furthermore, researchers employed fitted analytical approaches because of the difficulty of obtaining accurate solutions to these types of problems. Some of these methods are reproducing kernel Hilbert space method [ 7 ], Nyström method [ 38 ], Touchard polynomials method [ 2 ], Tau method [ 20 , 32 ], Collocation and Kantorovich methods [ 37 ], Galerkin method [ 12 , 41 , 43 ], Boole collocation method [ 14 ], parameterization method [ 17 ], Legendre collocation matrix method[ 44 ], variational iteration technique [ 19 ]. The increasing interest in recent years is not limited to only FIDEs, but also the numerical solutions of linear and nonlinear Volterra or Volterra-Fredholm integro-differential equations are increasing in popularity.…”