The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

Displaying similar documents to “On well-posedness of the nonlocal boundary value problem for parabolic difference equations.”

Implicit difference schemes for mixed problems related to parabolic functional differential equations

Milena Netka (2011)

Annales Polonici Mathematici

Similarity:

Solutions of initial boundary value problems for parabolic functional differential equations are approximated by solutions of implicit difference schemes. The existence and uniqueness of approximate solutions is proved. The proof of the stability is based on a comparison technique with nonlinear estimates of the Perron type for given operators. It is shown that the new methods are considerably better than the explicit difference schemes. Numerical examples are presented.

Comparison of explicit and implicit difference schemes for parabolic functional differential equations

Zdzisław Kamont, Karolina Kropielnicka (2012)

Annales Polonici Mathematici

Similarity:

Initial-boundary value problems of Dirichlet type for parabolic functional differential equations are considered. Explicit difference schemes of 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 the assumptions on the regularity of the given functions are the same for both...

Generalized method of lines for first order partial functional differential equations

W. Czernous (2006)

Annales Polonici Mathematici

Similarity:

Classical solutions of initial boundary value problems are approximated by solutions of associated differential difference problems. A method of lines for an unknown function for the original problem and for its partial derivatives with respect to spatial variables is constructed. A complete convergence analysis for the method is given. A stability result is proved by using differential inequalities with nonlinear estimates of the Perron type for the given operators. ...