Abstract:
The aim of thesis is to develop explicit higher order stochastic Runge-Kutta methods of Stratonovich stochastic differential equations (SDEs). In this thesis, new higher order stochastic Runge-Kutta type methods SRK(M), SRK(LS1), SRK(KPS), and SRK(LS2) are developed for the numerical solution of Stratonovich stochastic differential equations. We first consider the analytical solution of the SDEs for Geometric Brownian Motion, the Ornstein-Uhlenbeck process, Hyperbolic Sine process, and the Cox-Ingersoll- Ross process. The above methods are applied to these SDEs and the numerical results are presented. Our main result is that of these methods only the SRK(LS1) and SRK(LS2) methods have higher strong order of convergence than the corresponding pure methods that these methods originated from.
