Ukrainian Mathematical Journal

, Volume 65, Issue 10, pp 1514–1541 | Cite as

Method of Lines for Quasilinear Functional Differential Equations

  • W. Czernous
  • Z. Kamont

We give a theorem on the estimation of error for approximate solutions to ordinary functional differential equations. The error is estimated by a solution of an initial problem for a nonlinear functional differential equation. We apply this general result to the investigation of convergence of the numerical method of lines for evolution functional differential equations. The initial boundary-value problems for quasilinear equations are transformed (by means of discretization in spatial variables) into systems of ordinary functional differential equations. Nonlinear estimates of the Perron-type with respect to functional variables for given operators are assumed. Numerical examples are given.


Cauchy Problem Classical Solution Parabolic Problem Maximal Solution Condition Deal 
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© Springer Science+Business Media New York 2014

Authors and Affiliations

  • W. Czernous
    • 1
  • Z. Kamont
    • 1
  1. 1.Faculty of Mathematics and Computer ScienceUniversity of Warmia and MazuryOlsztynPoland

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