Multi-step methods for numerical solutions of multiplicative initial value problems

In this thesis, multi-step methods based on unconditionally stable multiplicative harmonic and counter-harmonic means are developed in order to calculate numerical solutions of multiplicative initial value problems. This thesis consists of four chapters. In the first part, which is called the introduction part, the literature information about the subject of the research is given. In the second part, some basic concepts about multiplicative algebraic operations, derivative, integral and multiplicative numerical analysis are given. In the third chapter, Runge-Kutta methods based on multiplicative harmonic and counter-harmonic means have been developed in order to obtain numerical solutions of multiplicative initial value problems. In addition, stability analysis and some numerical applications are performed in this section. Thus, it can be said that unconditionally stable and error minimizing methods are introduced.