Laguerre-type orthogonal polynomials and transformation of the Chebyshev nodes

In many numerical methods a real domain \(\Omega\) has to be discretized with a mesh of nodes and the choice of this mesh can influence the convergence and the accuracy of the method. One example is the pseudospectral method for delay differential equations with finite or infinite delay.

During the seminar two classes of nodes are shown and analyzed: the zeros of the Laguerre-type orthogonal polynomials, i.e., orthogonal polynomials with respect to the weight \(\frac{1}{\Gamma(\alpha+1)} x^\alpha e^{-x} + N\delta(x)\), and the extremal Chebyshev nodes transformed with a nonlinear function from \([-1,0]\) to \((-\infty,0]\).