Delay i̇ntegro-diferansiyel denklem sistemlerinin sayisal çözümleri ve uygulamalari için Chelyshkov matris metodu

The aim of this thesis is to obtain solutions of delay differential equations, delay integro-differential equantions and their systems with variable coefficients that have wide applications in the field of biology, ecology, engineering and other related scientific areas, by using a matrix collocation method based on Chelyshkov polynomials. By the used matrix collocation method, such differential equations or systems are converted into an algebraic equations system. Thus, it is enabled us to solve them by developed numerical scheme on the basis of matix collocation method. Moreover, the obtained solutions are improved by using residual function. This thesis consists of five chapters. In the first chapter, the variety of differential equations and their application areas have been reviewed.In the second chapter, the definitions about the governing differential equations and the studies on these equations, which are previously made, has been expressed. Firstly, type of diferential equations and their systems to be solved are explained, and the fundamental matrix relations on these equations are given in the third chapter. Then, error analysis has been made for the solution method. In the fourth chapter, examples of related solution method are given. The obtained solutions are compared with the solutions obtained from other methods, or exact solutions. These are tested with the help of tables and figures. Tables and figures display that the matrix method works properly and effectively for each problem type, which is verified with the obtained results.Lastly, In the fifth chapter, conclusion and proposal about solution method are given.