A finite differences method for a two-dimensional nonlinear hyperbolic equation in a class of discontinuous functions

RASULOV M., Coskun E., SINSOYSAL B.

APPLIED MATHEMATICS AND COMPUTATION, cilt.140, ss.279-295, 2003 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 140
  • Basım Tarihi: 2003
  • Doi Numarası: 10.1016/s0096-3003(02)00225-4
  • Dergi Adı: APPLIED MATHEMATICS AND COMPUTATION
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.279-295
  • Anahtar Kelimeler: shook waves, numerical modelling in a class of discontinuous functions
  • Karadeniz Teknik Üniversitesi Adresli: Evet

Özet

A numerical scheme is proposed for a scalar two-dimensional nonlinear first-order wave equation with both continuous and piecewise continuous initial conditions. It is typical of such problems to assume formal solutions with discontinuities at unknown locations, which justifies the search for a scheme that does not rely on the regularity of the solution. To this end, an auxiliary problem which is equivalent to, but has more advantages then, the original system is formulated and shown that regularity of the solution of the auxiliary problem is higher than that of the original system. An efficient numerical algorithm based on the auxiliary problem is derived. Furthermore, some results of numerical experiments of physical interest are presented. (C) 2002 Elsevier Science Inc. All rights reserved.