An operator-difference scheme for abstract Cauchy problems

Ashyralyev A., Koksal M. E., Agarwal R. P.

COMPUTERS & MATHEMATICS WITH APPLICATIONS, cilt.61, sa.7, ss.1855-1872, 2011 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 61 Sayı: 7
  • Basım Tarihi: 2011
  • Doi Numarası: 10.1016/j.camwa.2011.02.014
  • Dergi Adı: COMPUTERS & MATHEMATICS WITH APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1855-1872
  • Ondokuz Mayıs Üniversitesi Adresli: Hayır

Özet

An abstract Cauchy problem for second-order hyperbolic differential equations containing the unbounded self-adjoint positive linear operator A(t) with domain in an arbitrary Hilbert space is considered. A new second-order difference scheme, generated by integer powers of A(t), is developed. The stability estimates for the solution of this difference scheme and for the first- and second-order difference derivatives are established in Hilbert norms with respect to space variable. To support the theoretical statements for the solution of this difference scheme, the numerical results for the solution of one-dimensional wave equation with variable coefficients are presented. (C) 2011 Elsevier Ltd. All rights reserved.