On the Stability of Hyperbolic Equations With Unbounded Time Delay Term

Key Points

• To establish a stability theorem for hyperbolic equations involving unbounded time delay in a Hilbert space.
• Developed a stability theorem for the initial value problem of hyperbolic equations.
• Introduced a second order of accuracy difference scheme for approximation.
• Proved stability of the proposed difference scheme.
• Demonstrated stability for hyperbolic equations with unbounded time delay.
• Confirmed accuracy of the difference scheme in approximating solutions.