The method of non-local transformations: Applications to blow-up problems

被引：4

作者：

Polyanin, A. D. ^{[1
,2
,3
]}

Shingareva, I. K. ^{[4
]}

机构：

[1] RAS, Inst Problems Mech, 101 Vernadsky Ave,Bldg 1, Moscow 119526, Russia

[2] Natl Res Nucl Univ MEPhI, 31 Kashirskoe Shosse, Moscow 115409, Russia

[3] Bauman Moscow State Tech Univ, 5 Second Baumanskaya St, Moscow 105005, Russia

[4] Univ Sonora, Blvd Luis Encinas & Rosales S-N, Hermosillo 83000, Sonora, Mexico

来源：

VI INTERNATIONAL CONFERENCE PROBLEMS OF MATHEMATICAL PHYSICS AND MATHEMATICAL MODELLING | 2017年 / 937卷

关键词：

nonlinear differential equations; non-local transformations; blow-up problems; numerical solutions; Painleve equations; NUMERICAL-INTEGRATION; TIME;

D O I：

10.1088/1742-6596/937/1/012042

中图分类号：

O59 [应用物理学];

学科分类号：

摘要：

The method for numerical integration of Cauchy problems for ODEs with blowup solutions is described. It is based on introducing a new non-local variable that reduces a single nth-order ODE to a system of first-order coupled ODEs. This method leads to problems whose solutions are presented in parametric form and do not have blowing-up singular points; therefore the standard fixed-step numerical methods can be applied. The efficiency of the proposed method is illustrated with two test problems. It is shown that the first Painleve equation with suitable initial conditions have non-monotonic blow-up solutions.

引用

页数：9

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