Boole collocation method for the approximate solutions of Volterra-Fredholm integro-differential equations and rezidüel error analysis

This aim of the thesis is obtain the approximate solutions of the VolterraFredholm integro-differential equations by using the Boole collocation method. In this method, the problem given as a linear algebraic equation is transformed into a matrix equation with Boole polinomial, its derivatives and collocation points. Then, Boole coefficients are obtained from the solution of this matrix equation. The approximate solution is in the truncated Boole series form in the interval [𝑎, 𝑏]. The thesis consists of six chapters. In the first chapter, the emergence of the Volterra-Fredholm integro-differential equations, their using areas and classes are mentioned and the source information about their solution are given. In the second chapter, source information are given and historical development and features of Boole polynomial are mentioned. In the third chapter, Boole collocation method is presented. In the fourth chapter, the error estimated based on the Residual dunctions has been developed to show the accuracy of the Boole collocation method. In fifth chapter, Boole collocaiton method is applied to numerical examples and the results are compared in the table and figures. In the sixth chapter, the results are interpreted and future studies that can be done with this method are specified. Keywords: Boole polynomial, Volterra-Fredholm integro-differential equations, collocation points, Residual error analysis