Solutions based on bell polynomials of systems of functional volterra-fredholm type integro-differential equations with delays.

In this thesis, a matrix-collocation method is applied to obtain the solutions of ordinary differential equations, Fredholm Volterra type integro-differential equations, linear variable coefficients mixed delay Fredholm Volterra integro differential equations,funcitonal delay Volterra integro equaitons and differential system which take an important place in physics , chemistry, mechanics, engineering and other science branches by using Bell polynomials.In the used method, the coefficients are reduced to the matrix form and the approximate solution of the problem is reached. In addition, error analysis with the aid of residual function has been performed to determine error bounds of the obtained approximate solutions. The thesis consists of five chapters. In the first chapter, the usage areas and the emergence of functional differential equations are examined. In the second chapter, general information is given; resource descriptions, definition of Bell polynomials, recurrence relations and graphics are given. In the third chapter, the matrix-collocation methods are explained by using the basic matrix relations for differential equations in every section of chapter. Behind, an error analysis based on residual functional for the solution method is performed. In the fourth chapter, numerical examples are given for each section. The results are shown in tables and figures. In tables, the numerical solutions and exact solutions together with absolute errors are provided. Finally, in the fifth chapter, conclusions and recommendations are given.