Abstract
The Cauchy problem for abstract telegraph equations \({\frac{d^{2}u(t)}{dt^{2}}}+\alpha{\frac{du(t)}{dt}}+Au(t)+\beta u(t)= f(t)\) (\(0\leq t\leq T\)), \(u(0)=\varphi\), \(u^{\prime}(0)=\psi \) in a Hilbert space H with the self-adjoint positive definite operator A is studied. Stability estimates for the solution of this problem are established. The first and second order of accuracy difference schemes for the approximate solution of this problem are presented. Stability estimates for the solution of these difference schemes are established. In applications, two mixed problems for telegraph partial differential equations are investigated. The methods are illustrated by numerical examples.
Highlights
Hyperbolic partial differential equations arise in many branches of science and engineering, e.g., electromagnetic, electrodynamics, thermodynamics, hydrodynamics, elasticity, fluid dynamics, wave propagation, materials science
Stability estimates for the solution of this problem are established
The comparison convinces us that the finite difference scheme method of the second order of approximation gives better results
Summary
Hyperbolic partial differential equations arise in many branches of science and engineering, e.g., electromagnetic, electrodynamics, thermodynamics, hydrodynamics, elasticity, fluid dynamics, wave propagation, materials science. Stability estimates for the solution of difference schemes for the two mixed problems for telegraph partial differential equations are established. Proof Problem ( ) can be written in the abstract form ( ) in Hilbert space L ( ) with self-adjoint positive definite operator A = Ax defined by formula n
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
