Adi diferensiyel denklemlerin nümerik çözümleri

Since ordinary differential equations are useful in modelling the behavior of many physical processes, methods of solution for these equations are of great importance to engineers and scientists. Even though well-known ana lytical techniques can solve many important differential equations, a greater number of physically significant differential equations can not be solved using these techniques. Fortunately, the solutions of these equations can usually be generated numerically. There are many methods for finding approximate solutions to differential equations. Throughout the thesis, numerical techniques for ordinary differen tial equations are considered. In the first chapter, basic concepts which are going to be used are given. Second chapter contains numerical methods, all of which do not generate exact solutions, only approximate ones. Finally, in the last chapter a new numerical integration technique inspired by the Runge- Kutta method to solve the initial value problem is given. The method pre sented adds higher order derivative terms to the Runge-Kutta stage equations resulting in a higher order method without increasing the number of stages. Keywords: Ordinary Differential Equations, Numerical Analysis, Runge-Kutta Method. IV