ISSN:
1618-3932
Keywords:
Finite difference
;
fixed-point theory
;
pseudo-parabolic system
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract In this paper, we deal with the finite difference method for the initial boundary value problem of the nonlinear pseudo-parabolic system $$\begin{gathered} ( - 1)^M u_t + A(x,t,u,u_x , \cdots ,u_{x^{2M} } )u_{x^{2M} _t } = F(x,t,u,u_x , \cdots ,u_{x^{2M} } ), \hfill \\ u_{x^k } (0,t) = \psi _{0k} (t),u_{x^k } (L,t) = \psi _{1k} (t),k = 0,1, \cdots ,{\rm M} - 1, \hfill \\ u(x,0) = \phi (x), \hfill \\ \end{gathered} $$ in the rectangular domainQ T =[0≤X≤L, 0≤t≤T], whereu(x,t)=(u 1(x,t),u 2(x,t), ...,u m (x,t)),φ(x),ψ 0k (t),ψ 1k (t),F(x,t,u,u x , ...,u x 2m) arem-dimensional vector functions, andA(x,t,u,u x , ...,u x 2m is anm×m positive definite matrix. The existence and uniqueness of solution for the finite difference system are proved by the fixed-point theory. Stability, convergence and error estimates are derived.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02011192
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