A new method for computing a solution of the Cauchy problem with polynomial data for the system of crystal optics


Yakhno V., Altunkaynak M.

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, vol.87, no.7, pp.1469-1484, 2010 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 87 Issue: 7
  • Publication Date: 2010
  • Doi Number: 10.1080/00207160802380926
  • Journal Name: INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1469-1484
  • Keywords: analytical method, system of crystal optics, initial value problem, polynomial solutions, symbolic computations, symmetric hyperbolic system
  • Dokuz Eylül University Affiliated: Yes

Abstract

A new analytical method for solving an initial value problem (IVP) for the system of crystal optics with polynomial data and a polynomial inhomogeneous term is suggested. The found solution of the IVP is a polynomial. Theoretical and computational analysis of polynomial solutions and their comparison with non-polynomial solutions corresponding to smooth data are given. The applicability of polynomial solutions to physical processes is discussed. An implementation of this method has been made by symbolic computations in Maple 10.