Thesis
On absorbing areas of planar quadratic maps.
The numerical solution of fuzzy differential equations using linear multistep methods.
Cyclic phenomena for composition operators.
On the volume and integral points of a polyhedron in R n.
About the solutions of Lyapunov Equations.
The main purpose of this work can be divided in to three aspects. First, a study of the existence and uniqueness of the solution for special types of linear operator equations, namely the Lyapunov Equation. Second, a discussion of the range for the quaii-Jordan*-derivation. Third, some special types of Lyapunov Equation, namely Stein Equation.
Solvability and controllability of semilinear initial value control problem via semigroup approach
A novel approach for deriving some Runge-Kutta methods.
The objective of this thesis studying and deriving with some modification as a new approach of Runge-Kutta method including explicit, semi-explicit and implicit methods as well as studying stability of convergence of these methods. Also, one of most important themes of the thesis is to introduce variable step size and variable order methods using an extrapolation method which has the utility of controlling the local truncation error to be less than a prespecified tolerance error.