A solution method for autonomous first-order algebraic partial differential equations

被引：9

作者：

Grasegger, Georg ^{[1
]}

Lastra, Alberto ^{[2
]}

Rafael Sendra, J. ^{[2
]}

Winkler, Franz ^{[1
]}

机构：

[1] Johannes Kepler Univ Linz, DK Computat Math RISC, Linz, Austria

[2] Univ Alcala, Dpto Fis & Matemat, Ap Correos 20, E-28871 Madrid, Spain

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2016年 / 300卷

基金：

奥地利科学基金会;

关键词：

Partial differential equations; Algebraic hypersurface; Rational parametrization; Complete solution; RATIONAL GENERAL-SOLUTIONS; PARAMETRIZATION;

D O I：

10.1016/j.cam.2015.12.030

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we present a procedure for solving first-order autonomous algebraic partial differential equations in an arbitrary number of variables. The method uses rational parametrizations of algebraic (hyper)surfaces and generalizes a similar procedure for first-order autonomous ordinary differential equations. In particular we are interested in rational solutions and present certain classes of equations having rational solutions. However, the method can also be used for finding non-rational solutions. (C) 2016 Elsevier B.V. All rights reserved.

引用

页码：119 / 133

页数：15

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