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Sunday Olanrewaju Agboola 2 Olajide Ibikunle and 3 Balami H. Msiralia

**keywords:** Infinitesimal Generator, Uniformization Method, Runge-Kutta Methods, the Adams Formula, Backward Differentiation Formulae

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 ๐ denoted๐ FUW Trends in Science & Technology Journal, www.ftstjournal.com e-ISSN: 24085162; p-ISSN: 20485170; August, 2022: Vol. 7 No. 2 pp. 885-889 (๐) 885 , a row vector whose ๐ ๐กโ component is the probability that the Markov chain is in state ๐ at time step ๐, is the iterative solution methods for transient distribution in Markov chain. The solutions of transient distribution in Markov chain using uniformization methods for large state spaces have been investigated in this study, in order to provide some insight into the solutions of transient distribution in Markov chain using uniformization methods for large state spaces, which produce a significantly more accurate response 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. Our goal is to compute solutions and algorithms for large state spaces using uniformization methods, which begin with an initial estimate of the solution vector and then alter it in such a way that it gets closer and closer to the true solution with each step or iteration, saving time. Matrices operations, such as multiplication with one or more vectors, are performed using Markov chain laws, theorems, and formulas. For an illustrative example, the transient distribution vectorโs๐ (๐) , ๐ = 1, 2, โฆ, ; the value of๐พ, the number of terms to be included in the summation are acquired, and the technique is well presented.