Constancy Added Space Extension and Kronecker Power Series Kernel Separation for One Variable Conical ODEs

摘要

This work focuses on the probabilistic evolution approach (PEA) to a one unknown conical ODE with accompanying initial conditions. We use the constancy added space extension (CASE) to get rid of zeroth Kronecker power coefficient. CASE brings flexibilities to change the structure of the first Kronecker power coefficient matrix such that the solution of the PEA equations have a Kronecker power series representation where the summand's (kernel) temporal behavior appears only in a scalar factor while the remaining factor having time independent matrix algebraic structure. The paper is designed to be in conceptual level by skipping the implementations which is given in a separate paper.