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

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