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Two new approaches for construction of the high order of accuracy difference schemes for hyperbolic differential equations

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  • Allaberen Ashyralyev
  • Pavel E. Sobolevskii

Abstract

We consider the abstract Cauchy problem for differential equation of the hyperbolic type v ″ ( t ) + A v ( t ) = f ( t ) ( 0 ≤ t ≤ T ), v ( 0 ) = v 0 , v ′ ( 0 ) = v ′ 0 in an arbitrary Hilbert space H with the selfadjoint positive definite operator A . The high order of accuracy two-step difference schemes generated by an exact difference scheme or by the Taylor decomposition on the three points for the numerical solutions of this problem are presented. The stability estimates for the solutions of these difference schemes are established. In applications, the stability estimates for the solutions of the high order of accuracy difference schemes of the mixed-type boundary value problems for hyperbolic equations are obtained.

Suggested Citation

  • Allaberen Ashyralyev & Pavel E. Sobolevskii, 2005. "Two new approaches for construction of the high order of accuracy difference schemes for hyperbolic differential equations," Discrete Dynamics in Nature and Society, Hindawi, vol. 2005, pages 1-31, January.
    • Handle: RePEc:hin:jnddns:175341
    DOI: 10.1155/DDNS.2005.183
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    Cited by:

    1. Allaberen Ashyralyev & Deniz Agirseven, 2019. "Bounded Solutions of Semilinear Time Delay Hyperbolic Differential and Difference Equations," Mathematics, MDPI, vol. 7(12), pages 1-38, December.
    2. Akgül, Ali & Modanli, Mahmut, 2019. "Crank–Nicholson difference method and reproducing kernel function for third order fractional differential equations in the sense of Atangana–Baleanu Caputo derivative," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 10-16.

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