Developing an SL(2, R) Lie-group shooting method for a singular φ-Laplacian in a nonlinear ODE

被引：7

作者：

Liu, Chein-Shan ^{[1
]}

机构：

[1] Natl Taiwan Univ, Dept Civil Engn, Taipei 10764, Taiwan

来源：

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2013年 / 18卷 / 09期

关键词：

Singular phi-Laplacian; Regular phi-Laplacian; SL(2; R) Lie-group shooting method; Relativistic pendulum; BOUNDARY-VALUE-PROBLEMS; PERIODIC-SOLUTIONS; PENDULUM;

D O I：

10.1016/j.cnsns.2012.12.021

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the present paper, we develop an SL(2, R) Lie-group shooting method for a regular or singular phi-Laplacian in a nonlinear ordinary differential equation (ODE). By using the closure property of the Lie-group, one-step Lie-group transformation between the boundary values at two ends is established. Hence, we can derive a closed-form formula in terms of r is an element of [0, 1] to determine the missing left-boundary condition by matching the right-boundary condition through a few iterations. The present method is easy to numerical implementation with a cheap computational cost. Numerical examples are examined to show that the present SL(2, R) Lie-group shooting method is effective to treat the regular and singular phi-Laplacian with a high accuracy. (C) 2012 Elsevier B. V. All rights reserved.

引用

页码：2327 / 2339

页数：13

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