The Application of Runge-Kutta and Backward Differentiation Methods for Solving Transient Distribution in Markov Chain

The computation of state probability distributions at an arbitrary point in time, which in the case of a discrete-time Markov chain means finding the distribution at some arbitrary time step n de noted π(n), a row vector whose ith component is the probability that the Markov chain is in state i at time step n, is the iterative solution methods for transient distribution in Markov chain. The solutions of transient distribution in Markov chain using Euler and trapezoid methods have been investigated in this study, in order to provide some insight into the solutions of transient distribution in Markov chain, which produce a significantly more accurate re sponse in less time for some types of situations and also tries to get to the end result as quickly as possible while the solution must be computed when a specified number of well-defined stages have been completed.