The Lie-group Shooting Method for Radial Symmetric Solutions of the Yamabe Equation

• 作者: M.Hajiketabi R.A.Van Gorder S.Abbasbandy
• 来源期刊: 工程与科学中的计算机建模(英文)
• 学科: 数学
• 关键词: Yamabe EQUATION nonlinear singularly BOUNDARY value problem group PRESERVING scheme Lie-group SHOOTING method
• 年，卷（期）: 2015,（4）
• 页码范围: 329-351
• 页数: 23页
• 分类号: O17

摘要

We transform the Yamabe equation on a ball of arbitrary dimension greater than two into a nonlinear singularly boundary value problem on the unit interval[0;1].Then we apply Lie-group shooting method(LGSM)to search a missing initial condition of slope through a weighting factor r 2(0;1).The best r is determined by matching the right-end boundary condition.When the initial slope is available we can apply the group preserving scheme(GPS)to calculate the solution,which is highly accurate.By LGSM we obtain precise radial symmetric solutions of the Yamabe equation.These results are useful in demonstrating the utility of Lie-group based numerical approaches to solving nonlinear differential equations.