Fundamental matrix properties of charlier polynomials and aplications to functional integro-differential equations

In this study, a matrix-collocation method based on Charler polynomials together with Taylor polynomials, Stirling numbers and factorial poynomials is developed to solve functional differential and Volterra-Fredholm type integro-differential equations with mixed constant delays under the inital-boundary conditions. The used method reduces the solution of problem to the solution of a matrix equation and hence the approximate solution of the problem is obtained. Besides, the parameter- in Charlier polynomials is used for obtaining the appropriate solutions. An error analysis related with the residual function and the mean-value theorem is implemented and some examples are presented. The obtained results are demonstrated by tables and graphics; the usuability and efficiency of the method are observed. The thesis consists of five chapters. In the first chapter, the fundamental knowledges about functional differential and integro-differential equations are examined. In the second chapter, the general information related to the Stirling numbers, factorial polynomial and Charlier polynomial is given; the fundamental problem along with source data is established. In the third chapter, the Charlier matrix-collocation methods are developed by using the basic matrix relations for differential, delay differential and integral parts in the equation.and then, an error analysis based on residual function and the mean-value theorem for the solution is performed. In the fourth chapter, some numerical examples are given for each section. The results are supported by tables and figures. In tables and figures, the obtained solutions and exact solutions together with absolute errors are compared. Finally, in the fifth chapter, conclusions and recommendations are given.