Journal
COMPUTERS & MATHEMATICS WITH APPLICATIONS
Volume 61, Issue 7, Pages 1855-1872Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.camwa.2011.02.014
Keywords
Second-order hyperbolic equation; Difference scheme; Unconditionally stable; Stability; Initial-value problem; Variable coefficient; Numerical solution
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Funding
- Scientific and Technological Research Council of Turkey (TUBITAK) [Bideb-2219]
- TURKPETROL foundation
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An abstract Cauchy problem for second-order hyperbolic differential equations containing the unbounded self-adjoint positive linear operator A(t) with domain in an arbitrary Hilbert space is considered. A new second-order difference scheme, generated by integer powers of A(t), is developed. The stability estimates for the solution of this difference scheme and for the first- and second-order difference derivatives are established in Hilbert norms with respect to space variable. To support the theoretical statements for the solution of this difference scheme, the numerical results for the solution of one-dimensional wave equation with variable coefficients are presented. (C) 2011 Elsevier Ltd. All rights reserved.
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