Approximate solutions of high order fredholm type linear integro-differential equations by abel matrix method

This thesis uses a matrix method based on Abel polynomials and collocation points to approximate Fredholm integrodifferential equations. In this method, the equation in subject transforms matrix equation using Abel polynomials and calculation method. After solving this matrix equation, the unknown Abel coefficients are gathered, and the approximate solution is obtained. This thesis contains five chapters. The first chapter explains differential equations, integral equations, and integrodifferential equations and their usage areas. The second chapter explains resource summary descriptions, definition, properties, and basic matrix relations of Abel polynomials. In the third chapter, the Abel matrix method and the fundamental matrix relations used in this method have been explained in detail; also, absolute error analyses are included. In the fourth chapter, some numeric examples regarding the solutions of Fredholm's integrodifferential equations are presented. Finally, the fifth chapter is the results