Journal of Mathematical Sciences

, Volume 77, Issue 5, pp 3399–3405 | Cite as

The FD method for first-order linear hyperbolic differential equations with piecewise smooth coefficients

  • V. L. Makarov
  • V. V. Vinokur


A justification of the differential-discrete FD method for solving one class of first-order linear partial differential equations with piecewise smooth coefficients, a right-hand side, and initial conditions is presented. The convergence rate of the method is shown to be limited exclusively by the smoothness of the input information. High accuracy, ease of algorithmic implementation, and feasibility of representation of results in an analytical form point to the advantage of the FD method over the other methods for the given class of problems. Bibliography:6 titles.


Differential Equation Partial Differential Equation Convergence Rate Analytical Form Input Information 
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    B. L. Rozhdestvensky and N. N. Yanenko,Systems of Quasilinear Equations [in Russian], Nauka, Moscow (1968).Google Scholar
  4. 4.
    V. L. Makarov, “On a functional-difference FD method of an arbitrary order of accuracy for solving the Sturm-Liouville problem with piecewise smooth coefficients,”Dokl. AN SSSR,320, No. 1, 34–39 (1991).MATHGoogle Scholar
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Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • V. L. Makarov
  • V. V. Vinokur

There are no affiliations available

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