Numerical Analysis and Applications

, Volume 2, Issue 1, pp 46–57 | Cite as

Implicit difference methods for Hamilton-Jacobi functional differential equations

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Abstract

Classical solutions of initial boundary value problems are approximated by solutions of associated implicit difference functional equations. A stability result is proved by using a comparison technique with nonlinear estimates of the Perron type for given functions. The Newton method is used to numerically solve nonlinear equations generated by implicit difference schemes. It is shown that there are implicit difference schemes which are convergent whereas the corresponding explicit difference methods are not. The results obtained can be applied to differential integral problems and differential equations with deviated variables.

Key words

initial boundary value problem functional differential equation implicit difference method Newton method 

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Copyright information

© Pleiades Publishing, Ltd. 2009

Authors and Affiliations

  1. 1.Institute of MathematicsUniversity of GdańskGdańskPoland

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