Probabilistic Evolution Approach to ODEs with Laurent Series Expandable Descriptive Functions

Abstract

This paper focuses on the recently developed Probabilistic Evolution Approach to the solution of explicit ODE(s) for the descriptive functions expandable to Laurent series. We deal with polar and essential type singularities which were assumed not to be arising in our previous studies where analyticity everywhere except infinity was assumed for the descriptive functions. The present approach imbeds the polar singularities to the state vector therefore extends the state space by one more dimension. Kronecker power expansion is used in the formulation and results are same except the multidimensionality and block structures in the algebra.