论文标题
光谱搭配解决方案用于二阶奇异sturm-liouville本本特征问题
Spectral Collocation Solutions to Second Order Singular Sturm-Liouville Eigenproblems
论文作者
论文摘要
我们相对使用一些经典的光谱搭配方法以及高表现的Chebfun算法，以计算具有分离的自我相互接触边界条件的二阶奇异sturm-liouville问题的特征。对于极限圈的非振荡和振荡案例，我们都特别注意。分析了一些“硬”基准问题，通常分析了通常的数值方法（f。d。，f。e。m。等）失败。对于非常具有挑战性的贝塞尔特征问题，我们将尝试找出起源中奇异性的来源和含义。对于Dunford和Schwartz引起的双重单数本本特征，我们试图找出连续频谱概念的确切含义。对于某些奇异问题，只有两类方法的双重方法会产生可靠的结果。
We comparatively use some classical spectral collocation methods as well as highly performing Chebfun algorithms in order to compute the eigenpairs of second order singular Sturm-Liouville problems with separated self-adjoint boundary conditions. For both the limit-circle non oscillatory and oscillatory cases we pay a particular attention. Some "hard" benchmark problems, for which usual numerical methods (f. d., f. e. m., etc.) fail, are analysed. For the very challenging Bessel eigenproblem we will try to find out the source and the meaning of the singularity in the origin. For a double singular eigenproblem due to Dunford and Schwartz we we try to find out the precise meaning of the notion of continuous spectrum. For some singular problems only a tandem approach of the two classes of methods produces credible results.
