Cosine Methods for Second-Order Hyperbolic Equations With Time-Dependent Coefficients

  title={Cosine Methods for Second-Order Hyperbolic Equations With Time-Dependent Coefficients},
  author={Laurence A. Bales and Yassilios A. Dougalis and Steven M. Serbin},
We analyze efficient, high-order accurate methods for the approximation of the solutions of linear, second-order hyperbolic equations with time-dependent coefficients. The methods are based on Galerkin-type discretizations in space and on a class of fourth-order accurate, two-step, cosine time-stepping schemes. Preconditioned iterative techniques are used to solve linear systems with the same operator at each time step. The schemes are supplemented by single-step high-order starting procedures… CONTINUE READING

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Publications referenced by this paper.
Showing 1-10 of 11 references


  • J. H. Brambl
  • H. Sammon, "Efficient higher order single step…
  • 1980
Highly Influential
6 Excerpts

Incomplete iteration for time-stepping a Galerkin method for a quasilinear parabolic problem,

  • J. Douglas, Jr., T. Dupont, R. E. Ewing
  • SIAM J. Numer. Anal., v
  • 1979
Highly Influential
4 Excerpts

Serbin, "Some cosine schemes for second-order systems of O.D.E.'s with time-varying coefficients,

  • S M.
  • SIAM J. Sei. Statist. Comput.. v
  • 1985

On efficient time-stepping methods for nonlinear partial differential equations,

  • R. E. Ewing
  • Compta. Math. Appl.,
  • 1980
1 Excerpt

Serbin, "An approximation theorem for second-order hyperbolic equations,

  • G. A. Baker, S.M.V.A. Dougalis
  • Numer. Math., v
  • 1980
2 Excerpts


  • G. A. Bake
  • H. Bramble, " Semidiscrete and single step fully…
  • 1979


  • G. A. Baker, V. A. Dougali
  • M. Serbin, "High order accurate, two-step…
  • 1979
2 Excerpts

Rational approximation of trigonometric matrices with applications to second-order systems of differential equations," Appl

  • S. M. Serbin
  • Math. Comput., v. 5,
  • 1979


  • J. H. Bramble, A. H. Schatz, V. Thomé
  • B. Wahlbin, "Some convergence estimates for…
  • 1977
1 Excerpt

Solution of linear systems of equations: Iterative methods," Sparse Matrix Techniques (V

  • O. Axelsson
  • A. Barker, ed.), Lecture Notes in Math., vol. 572…
  • 1976
1 Excerpt

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