Probabilistic evolution approach for the solution of explicit autonomous ordinary differential equations. Part 1: Arbitrariness and equipartition theorem in Kronecker power series


Gozukirmizi C., Demiralp M.

JOURNAL OF MATHEMATICAL CHEMISTRY, cilt.52, sa.3, ss.866-880, 2014 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 52 Konu: 3
  • Basım Tarihi: 2014
  • Doi Numarası: 10.1007/s10910-013-0298-5
  • Dergi Adı: JOURNAL OF MATHEMATICAL CHEMISTRY
  • Sayfa Sayıları: ss.866-880

Özet

Probabilistic evolution approach is a newly developed theory which may be utilized for the solution of ordinary differential equations. The approach may directly be applied for initial value problems of explicit first order autonomous ordinary differential equation sets with analytic right hand side functions. Analyticity plays an important role since it facilitates the expansion into direct power series which is the key element of the approach. Direct power series appear not only in all applications of probabilistic evolution but also show themselves as a promising tool for novel approximation methods. In this work, similarities and differences between Taylor series and direct power series are rigorously studied. Arbitrariness in transposed vector coefficients of direct power series is detailed. Equipartition theorem of direct power series is conjectured and proven in order to obtain unique transposed vector coefficients.