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Numerical method of lines for evolution functional differential equations
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Z. Kamont
Published/Copyright:
May 27, 2011
Abstract
We give a theorem on error estimates of approximate solutions for the ordinary functional differential equation. The error is estimated by a solution of an initial problem for nonlinear differential functional equation. We apply this general result to the investigation of the convergence of the numerical method of lines generated by evolution functional differential equations. Initial boundary value problems for Hamilton Jacobi functional differential equations and parabolic functional differential problems are considered. Nonlinear estimates of the Perron type with respect to the functional variable for given operators are assumed.
Keywords:: numerical method of lines; functional differential equations; stability and convergence; differential inequalities
Received: 2010-06-30
Revised: 2011-03-01
Published Online: 2011-05-27
Published in Print: 2011-May
© de Gruyter 2011
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Articles in the same Issue
- Approximation of the biharmonic problem using P1 finite elements
- L2 error estimates for a nonstandard finite element method on polyhedral meshes
- Higher order Galerkin time discretizations and fast multigrid solvers for the heat equation
- Numerical method of lines for evolution functional differential equations
Keywords for this article
numerical method of lines;
functional differential equations;
stability and convergence;
differential inequalities
Articles in the same Issue
- Approximation of the biharmonic problem using P1 finite elements
- L2 error estimates for a nonstandard finite element method on polyhedral meshes
- Higher order Galerkin time discretizations and fast multigrid solvers for the heat equation
- Numerical method of lines for evolution functional differential equations
