Probabilistic evolution theory for explicit autonomous ordinary differential equations: recursion of squarified telescope matrices and optimal space extension

Gozukirmizi C., Demiralp M.

JOURNAL OF MATHEMATICAL CHEMISTRY, cilt.56, sa.7, ss.1826-1848, 2018 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 56 Sayı: 7
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1007/s10910-017-0849-2
  • Dergi Adı: JOURNAL OF MATHEMATICAL CHEMISTRY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1826-1848
  • İstanbul Teknik Üniversitesi Adresli: Evet

Özet

Probabilistic evolution theory facilitates the solution of initial value problem of explicit autonomous ordinary differential equations with second degree multinomial right hand side functions. Its formulation has components we call telescope matrices. The matrices grow in size very rapidly and has many zeroes and repeating structures. In order to avoid the computational complexity coming from telescope matrices, squarified telescope matrices are utilized. Their calculation is through a recursion. This recursion has been used in several works by the authors and their colleagues but its proof was not given. This work gives the proof of the recursion and all the surrounding details. A second purpose of this work is to provide a method for most facilitative (optimal) space extension. Space extension is needed for using probabilistic evolution theory when degree of multinomiality of the right hand side functions is more than two. For this purpose, an approach using method of exhaustion (brute-force) is proposed.