A note on the second order of accuracy difference schemes for hyperbolic-parabolic equations in a Hilbert space. (English) Zbl 1069.65097

Ashyralyev, Allaberen; Yurtsever, Hasan A.

Ladde, G.S.(ed.) et al., Dynamic systems and applications. Volume 4. Proceedings of the 4th international conference, Morehouse College, Atlanta, GA, USA, May 21–24, 2003. Atlanta, GA: Dynamic Publishers (ISBN 1-890888-00-1/hbk). 556-562 (2004).

Summary: The non-local boundary value problem for hyperbolic-parabolic equations in a Hilbert space \(H\) is considered. Second-order of accuracy difference schemes approximately solving this boundary value problem are presented. Stability estimates for the solution of these difference schemes are established. In applications, the stability estimates for the solutions of the difference schemes of mixed type boundary value problems for hyperbolic-parabolic equations are obtained.
For the entire collection see [Zbl 1054.34001].

MSC:

65M06	Finite difference methods for initial value and initial-boundary value problems involving PDEs
35K90	Abstract parabolic equations
35L90	Abstract hyperbolic equations
35M10	PDEs of mixed type
34G10	Linear differential equations in abstract spaces
65J10	Numerical solutions to equations with linear operators
65M12	Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs

Keywords:

stability; non-local boundary value problem; hyperbolic-parabolic equations; Hilbert space; difference schemes