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A note on the difference schemes for hyperbolic equations

Author

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  • A. Ashyralyev
  • P. E. Sobolevskii

Abstract

The initial value problem for hyperbolic equations d 2 u ( t ) / d t 2 + A u ( t ) = f ( t ) ( 0 ≤ t ≤ 1 ) , u ( 0 ) = φ , u ′ ( 0 ) = ψ , in a Hilbert space H is considered. The first and second order accuracy difference schemes generated by the integer power of A approximately solving this initial value problem are presented. The stability estimates for the solution of these difference schemes are obtained.

Suggested Citation

  • A. Ashyralyev & P. E. Sobolevskii, 2001. "A note on the difference schemes for hyperbolic equations," Abstract and Applied Analysis, Hindawi, vol. 6, pages 1-8, January.
    • Handle: RePEc:hin:jnlaaa:694534
    DOI: 10.1155/S1085337501000501
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    Cited by:

    1. Ozgur Yildirim & Meltem Uzun, 2015. "On Third Order Stable Difference Scheme for Hyperbolic Multipoint Nonlocal Boundary Value Problem," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-16, July.

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