On the Second Order of Accuracy Difference Scheme for Hyperbolic Equations in a Hilbert Space

ABSTRACT

The initial-value problem for hyperbolic equation

in a Hilbert space H with the self-adjoint positive definite operators A(t) is considered. The second order of accuracy absolute stable difference scheme for approximately solving this abstract initial-value problem is presented. The stability estimates for the solution of this difference scheme and for the first- and second-order difference derivatives are established.

Keywords:

• Abstract hyperbolic equation
• Difference scheme
• Initial-value problem
• Stability

Mathematics Subject Classification (2000):

• 65J10
• 65M10
• 65M20

ACKNOWLEDGMENT

The authors would like to thank Prof. Dr. Pavel Sobolevskii (Jerusalem, Israel), for his helpful suggestions to the improvement of this paper.