Probabilistic evolution theory for the solution of explicit autonomous ordinary differential equations: squarified telescope matrices
Küçük Resim Yok
Tarih
2017
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Springer
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
Probabilistic evolution theory (PREVTH) is used for the solution of initial value problems of first order explicit autonomous ordinary differential equation sets with second degree multinomial right hand side functions. It is an approximation method based on Kronecker power series: a rewriting of multivariate Taylor series using matrices having certain flexible parameters. Kronecker power series have matrices which are called telescope matrices: matrices where j is the index of summation. The additive terms of each telescope matrix is formed through Kronecker product from both sides by Kronecker powers of identity matrices. Recently, squarification is proposed in order to avoid the growing of the matrices in size at each additive term of the series. This paper explains the squarification procedure: the procedure used in order to avoid Kronecker multiplications within PREVTH so that the sizes of the matrices do not grow and so that the amount of necessary computation is reduced. The recursion between squarified matrices is also given. As a numerical application, the solution of a H,non-Heiles system is provided.
Açıklama
Anahtar Kelimeler
Probabilistic evolution theory, Squarification, Kronecker power series, Initial value problem
Kaynak
Journal Of Mathematical Chemistry
WoS Q Değeri
Q2
Scopus Q Değeri
Q2
Cilt
55
Sayı
1
