TY - JOUR
T1 - On the stability of hyperbolic difference equations with unbounded delay term
AU - Ashyralyev, Allaberen
AU - Vlasov, Victor V.
AU - Ashyralyyev, Charyyar
N1 - Publisher Copyright:
© 2023, Sociedad Matemática Mexicana.
PY - 2023/7
Y1 - 2023/7
N2 - The paper studies the unconditionally stable difference scheme for the approximate solution of the hyperbolic differential equation with unbounded delay term {vtt(t)+A2v(t)=a(vt(t-w)+Av(t-w))+f(t),t∈(0,∞),v(t)=φ(t),t∈[-w,0]in a Hilbert space H with a self-adjoint positive definite operator A. The main theorem on unconditionally stability estimates for the solutions of this problem are established. Numerical results and explanatory illustrations are presented show the validation of the theoretical results.
AB - The paper studies the unconditionally stable difference scheme for the approximate solution of the hyperbolic differential equation with unbounded delay term {vtt(t)+A2v(t)=a(vt(t-w)+Av(t-w))+f(t),t∈(0,∞),v(t)=φ(t),t∈[-w,0]in a Hilbert space H with a self-adjoint positive definite operator A. The main theorem on unconditionally stability estimates for the solutions of this problem are established. Numerical results and explanatory illustrations are presented show the validation of the theoretical results.
KW - 35K60
KW - 35L20
KW - 39A30
KW - 65M06
KW - Difference scheme (DS)
KW - Hyperbolic equation (HE)
KW - Stability
KW - Unbounded delay term (UDT)
UR - http://www.scopus.com/inward/record.url?scp=85149937899&partnerID=8YFLogxK
U2 - 10.1007/s40590-023-00498-z
DO - 10.1007/s40590-023-00498-z
M3 - Article
AN - SCOPUS:85149937899
SN - 1405-213X
VL - 29
JO - Boletin de la Sociedad Matematica Mexicana
JF - Boletin de la Sociedad Matematica Mexicana
IS - 2
M1 - 27
ER -