Solutions of delayed integro differential equations using fubini polynomials

In this thesis, a matrix-sorting(collocation) method using the Fubini polynomial is developed to find the solutions of linear delay Fredholm type integro-differential equations and linear delay Volterra type integro-differential equations. In the used method, firstly Fubini polynomials, their derivatives and solutions are written in matrix forms. Then, the problem is reduced to a system of algebraic equations by using collocation points and matrix operations. This system of equations is also solved with the help of the MATLAB program, and the approximate solutions of the problem are obtained. In addition, when the exact solutions are not known, the residual error estimation method is presented to test the reliability of the solutions, and the error analysis of the obtained solutions is made with the help of the residual error function and the approximate error is improved. The thesis consists of six chapters. In the introduction section; differential equations and their subclasses and the aim of the thesis are mentioned. In the second part; general information, resource summaries and basic concepts of Fubini polynomials are given. In the third part; The solution method for delay Fredholm integro-differential equations and delayVolterra integro differential equations is shown by establishing basic matrix connections. In the fourth Chapter, an error analysis based on the residual function is made for the accuracy and validity of the solution method. In the fifth Chapter, numerical examples are given for each equation type. The results are shown in tables and figures. In addition, true absolute error, estimated absolute error and improved absolute errors are compared in tables. Finally, conclusions and recommendations are given in the sixth section.