Formal solutions of completely integrable Pfaffian systems with normal crossings

被引：2

作者：

Barkatou, Moulay A. ^{[1
,2
]}

Aroschek, Maximilian J. ^{[3
]}

Maddah, Suzy S. ^{[4
]}

机构：

[1] Univ Limoges, DMI, XLIM UMR 7252, 123 Ave Albert Thomas, F-87060 Limoges, France

[2] CNRS, 123 Ave Albert Thomas, F-87060 Limoges, France

[3] Max Planck Inst Informat, Saarland Informat Campus E1 4, D-66123 Saarbrucken, Germany

[4] Fields Inst, 222 Coll St, Toronto, ON M5T 3J1, Canada

来源：

JOURNAL OF SYMBOLIC COMPUTATION | 2017年 / 81卷

关键词：

Linear systems of partial differential equations; Pfaffian systems; Formal solutions; Rank reduction; Hukuhara-Turrittin's normal form; Normal crossings; ALGORITHM;

D O I：

10.1016/j.jsc.2016.11.018

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

In this paper, we present an algorithm for computing a fundamental matrix of formal solutions of completely integrable Pfaffian systems with normal crossings in several variables. This algorithm is a generalization of a method developed for the bivariate case based on a combination of several reduction techniques and is partially(2) implemented in the computer algebra system MAPLE. (C) 2016 Elsevier Ltd. All rights reserved.

引用

页码：41 / 68

页数：28

共 32 条

[1]

Abbas H., 2014, P INT S SYMB ALG COM, P312

[2]

Abbas H., 2014, P 39 INT S SYMB ALG, P320

[3]

BALSER W., 2000, Formal power series and linear systems of meromorphic ordinary differential equations

[4]

Barkatou A., 1995, Proceedings of the 1995 International Symposium on Symbolic and Algebraic Computation, ISSAC '95, P297, DOI 10.1145/220346.220385

[5] An algorithm computing the regular formal solutions of a system of linear differential equations [J].

Barkatou, M ;

Pflügel, E .

JOURNAL OF SYMBOLIC COMPUTATION, 1999, 28 (4-5) :569-587

[6]

Barkatou M., 2010, INT S SYMB ALG COMP, P7

[7]

Barkatou M., 2007, COMPUTER ALGEBRA, P22

[8]

Barkatou M.A., 2012, P INT S SYMB ALG COM, P43

[9] An algorithm to compute the exponential part of a formal fundamental matrix solution of a linear differential system [J].

Barkatou M.A. .

Applicable Algebra in Engineering, Communication and Computing, 1997, 8 (1) :1-23

[10] On k-simple forms of first-order linear differential systems and their computation [J].

Barkatou, Moulay A. ;

El Bacha, Carole .

JOURNAL OF SYMBOLIC COMPUTATION, 2013, 54 :36-58

← 1 2 3 4 →