Solutions of stochastic ordinary differential equations using variable step size Runge-Kutta methods

The main objective of this thesis is divided in to three directions which are: The first one is to study and overview the main and basic concepts of stochastic calculus, as well as, studying stochastic ordinary differential
equations. The second objective is to study explicit stochastic Runge-Kutta methods, then generalize this scheme for semi-explicit, implicit and mixed schemes and study theirs numerical stability. The third objective is to introduce variable step size method for solving stochastic ordinary differential equations, which has the utility of improving the accuracy of the obtained results