多二次方法离散的非线性椭圆型偏微分方程的延拓
Continuation for Nonlinear Elliptic Partial Differential Equations Discretized by the Multiquadric Method
AI总结：
本文采用多二次径向基函数方法离散非线性椭圆型偏微分方程，生成规模适中的非线性代数方程组，并利用标准延拓软件高效延拓，成功检测一维和二维分岔，以较少未知数实现高精度。
摘要：
多二次径向基函数（MQ）方法是一种具有全局基函数的无网格配置方法。已知该方法对插值问题具有指数收敛性。我们采用MQ方法离散非线性椭圆型偏微分方程。这产生了规模适中的非线性代数方程组，可通过标准延拓软件（如AUTO和CONTENT）高效地进行延拓。文中给出了在一维和二维偏微分方程中检测分岔的实例。这些实例表明，与文献中已知结果相比，在未知数较少的情况下实现了高精度。
英文摘要：
The Multiquadric Radial Basis Function (MQ) Method is a meshless collocation method with global basis functions. It is known to have exponentional convergence for interpolation problems. We descretize nonlinear elliptic PDEs by the MQ method. This results in modest size systems of nonlinear algebraic equations which can be efficiently continued by standard continuation software such as AUTO and CONTENT. Examples are given of detection of bifurcations in 1D and 2D PDEs. These examples show high accuracy with small number of unknowns, as compared with known results from the literature.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
