Unidirectional Semi-Analytic Continuation in the Probabilistic Evolution Approach to Van der Pol Equation

Abstract

Probabilistic Evolution Approach (PEA) is a method recently developed for the solution of explicit ODEs. There is now a comprehensive knowledge accumulation for PEA. It is well known that the PEA truncation approximants converge to a unique limit representing the solution of the considered ODE in a finite region of the complex planes of the unknowns. The complement of the union of these regions to entire complex plane(s) is the subject of analytic continuation. In this paper we focus on this issue for the Van der Pol Equation. Paper gives the importance rather to the formalism and conceptuality. True implementations are left to future works.