More Practicalization of Probabilistic Evolution Theory: Case Studies for the Squarification of Telescope Matrices

Kirkin M. E., Demiralp M.

11th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences (ICNPAA), La Rochelle, France, 4 - 08 July 2016, vol.1798 identifier identifier

  • Publication Type: Conference Paper / Full Text
  • Volume: 1798
  • Doi Number: 10.1063/1.4972669
  • City: La Rochelle
  • Country: France
  • Istanbul Technical University Affiliated: Yes


Probabilistic Evolution Theory (PREVTH) developed in quite recent Demiralp group studies, [1-18], takes us to analytic solutions for any given explicit first order ODE set, at least by using space extension concept for various purposes. These solutions have Kronecker power series structures with so-called coefficients, "Telescope Matrices", whose types for the jth coefficient is n x n(j) for an n unknown ODE set. Telescope matrices have sparsities which rapidly increases when j tends to grow unboundedly. We have quite recently developed a compaction method we have called "Squarification" to reduce computational complexity. The ODE set mentioned here is accompanied by appropriate initial conditions. We can give sufficient recalls to facilitate the reading of the paper. This paper takes the Van Der Pol ODE set to the focus on and PREVTH application is presented at both theoretical and numerical implementational respects.