Iterative methods for parabolic functional differential equations

Milena Matusik¹

¹ Institute of Mathematics University of Gdańsk Wit Stwosz Street 57 80-952 Gdańsk, Poland

Applicationes Mathematicae, Tome 40 (2013) no. 2, pp. 221-235

Résumé

This paper is concerned with iterative methods for parabolic functional differential equations with initial boundary conditions. Monotone iterative methods are discussed. We prove a theorem on the existence of solutions for a parabolic problem whose right-hand side admits a Jordan type decomposition with respect to the function variable. It is shown that there exist Newton sequences which converge to the solution of the initial problem. Differential equations with deviated variables and differential integral equations can be obtained from our general model by specializing given operators.

Détail

DOI : 10.4064/am40-2-5

Keywords: paper concerned iterative methods parabolic functional differential equations initial boundary conditions monotone iterative methods discussed prove theorem existence solutions parabolic problem whose right hand side admits jordan type decomposition respect function variable shown there exist newton sequences which converge solution initial problem differential equations deviated variables differential integral equations obtained general model specializing given operators