Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Difference schemes for fully nonlinear pseudo-hyperbolic systems

Difference schemes for fully nonlinear pseudo-hyperbolic systems The general difference schemes for the first boundary problem of the fully nonlinear pseudohyperbolic systems $$f(x,t,u,u_x ,u_{xx} ,u_t ,u_{tt} ,u_{xt} ,u_{xxt} ) = 0$$ are considered in the rectangular domainQ T ={0≤x≤l, 0≤t≤T}, whereu(x, t) andf(x, t, u, p 1,p 2,r 1,r 2,q 1,q 2) are twom-dimensional vector functions withm ≥ 1 for (x, t) ∈Q T andu, p 1,p 2,r 1,r 2,q 1,q 2 ∈R m . The existence and the estimates of solutions for the finite difference system are established by the fixed point technique. The absolute and relative stability and convergence of difference schemes are justified by means of a series of a prior estimates. In the present study, the existence of unique smooth solution of the original problem is assumed. The similar results for nonlinear and quasilinear pseudo-hyperbolic systems are also obtained. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Difference schemes for fully nonlinear pseudo-hyperbolic systems

Loading next page...
 
/lp/springer-journals/difference-schemes-for-fully-nonlinear-pseudo-hyperbolic-systems-PSSw6E0Xt2
Publisher
Springer Journals
Copyright
Copyright © 1991 by Science Press, Beijing, China and Allerton Press, Inc., New York, U.S.A.
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/BF02009682
Publisher site
See Article on Publisher Site

Abstract

The general difference schemes for the first boundary problem of the fully nonlinear pseudohyperbolic systems $$f(x,t,u,u_x ,u_{xx} ,u_t ,u_{tt} ,u_{xt} ,u_{xxt} ) = 0$$ are considered in the rectangular domainQ T ={0≤x≤l, 0≤t≤T}, whereu(x, t) andf(x, t, u, p 1,p 2,r 1,r 2,q 1,q 2) are twom-dimensional vector functions withm ≥ 1 for (x, t) ∈Q T andu, p 1,p 2,r 1,r 2,q 1,q 2 ∈R m . The existence and the estimates of solutions for the finite difference system are established by the fixed point technique. The absolute and relative stability and convergence of difference schemes are justified by means of a series of a prior estimates. In the present study, the existence of unique smooth solution of the original problem is assumed. The similar results for nonlinear and quasilinear pseudo-hyperbolic systems are also obtained.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Jul 14, 2005

References