Pell-lucas matrix-collocation method for solving volterra type functional integro-differential equations and applications

This thesis is about obtaining the solutions of ordinary differential equations, integro-differential equations, Volterra type integro-differential equations, linear differential-difference equations and integro-differential equations with proportional delays by a Pell-Lucas matrix collocation method. Nowadays researchers in engineering, chemistry, physics and other applied sciences encounter a lot of difficult problems due to various reasons arising from chemical, physical, mechanical properties of materials. Integro-differential equations with variable and proportional delays are commonly encountered but they are very difficult to solve, for this reason, a number of numerical methods to solve such type of equations have been developed by different researchers. In this thesis, a Pell-Lucas matrix-collocation method will be used as a numerical method to solve these mentioned problems. In this method, the coefficients of Pell-Lucas polynomials are transformed into a matrix form and consequently, the approximate solution is obtained. Furthermore, residual error and absolute error analysis methods are applied to check the accuracy of the solution. This thesis contains five chapters. The first chapter is about the emergence and application areas of functional differential equations. In the second chapter, the information and graphs of Pell-Lucas polynomials are given. Matrix-collocation method is given in chapter three, additionally, residual error analysis is explained by the means of the mean value theorem. The fourth chapter is about numerical examples together with their tables and graphics. Lastly, chapter five is about the conclusions. Consequently, this method can be applied to other different mathematical models. Keywords: Pell-Lucas polynomials, Matrix-collocation method, Volterra type integro-differential equations, Linear ordinary differential equations, Delay Integro-Differential Equations, Residual error analysis.