A New Unconditionally Stable Second Order of Accuracy Difference Scheme for the Time Delay Telegraph Equation
Ashyralyev A. Agirseven D. Turk K.
December 2025John Wiley and Sons Ltd
Mathematical Methods in the Applied Sciences
2025#48Issue 1816540 - 16551 pp.
In this paper, we study a new unconditionally stable second order of accuracy difference scheme for the approximate solution of the initial value problem for the time delay telegraph equation in a Hilbert space with self-adjoint positive definite operator. We prove the main theorem on stability of this difference scheme. As an application, we present absolutely stable difference schemes for the approximate solution of two initial-boundary value problems for one-dimensional delay telegraph equation with nonlocal conditions and multidimensional delay telegraph equation with Dirichlet condition. Finally, to support the theoretical result, a numerical example of the initial-boundary value problem for the two-dimensional delay telegraph equation with Dirichlet condition is presented.
delay telegraph equation , difference scheme , stability
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Department of Mathematics, Bahcesehir University, Istanbul, Turkey
Peoples Friendship University of Russia (RUDN University), Moscow, Russian Federation
Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Department of Mathematics, Trakya Univesity, Edirne, Turkey
Department of Mathematics
Peoples Friendship University of Russia (RUDN University)
Institute of Mathematics and Mathematical Modeling
Department of Mathematics
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