Method of lines for nonlinear first order partial functional differential equations

被引：0
作者：
Szafranska, A. [1 ]
机构：
[1] Gdansk Univ Technol, Dept Math & Numer Anal, PL-80952 Gdansk, Poland
来源：
BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN | 2013年 / 20卷 / 05期
关键词：
functional differential equations; initial value problems; method of lines; stability and convergence; NUMERICAL-METHOD;
D O I：
10.36045/bbms/1385390769
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Classical solutions of initial problems for nonlinear functional differential equations of Hamilton Jacobi type are approximated by solutions of associated differential difference systems. A method of quasilinearization is adopted. Sufficient conditions for the convergence of the method of lines and error estimates for approximate solutions are given. Nonlinear estimates of the Perron type with respect to functional variables for given operators are assumed. The proof of the stability of differential difference problems is based on a comparison technique. The results obtained here can be applied to differential integral problems and differential equations with deviated variables.
引用
收藏
页码：859 / 880
页数：22
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