Numerical methods for Hamilton Jacobi functional differential equations |
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Authors: | W?Czernous Email author" target="_blank">Z?KamontEmail author |
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Institution: | 1.Institute of Mathematics University of Gdańsk,Gdańsk,Poland |
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Abstract: | Initial and initial boundary value problems for first order partial functional differential equations are considered. Explicit
difference schemes of the Euler type and implicit difference methods are investigated. The following theoretical aspects of
the methods are presented. Sufficient conditions for the convergence of approximate solutions are given and comparisons of
the methods are presented. It is proved that assumptions on the regularity of given functions are the same for both the methods.
It is shown that conditions on the mesh for explicit difference schemes are more restrictive than suitable assumptions for
implicit methods. There are implicit difference schemes which are convergent and corresponding explicit difference methods
are not convergent. Error estimates for both the methods are construted. |
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