2020/09/02 by Maria Carmela De Bonis, Donatella Occorsio, De Bonis, Maria Carmela +3
Mathematics · #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.2009.01290
openalex publication_date 2020/09/02 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
In order to solve Prandtl-type equations we propose a collocation-quadrature\nmethod based on VP filtered interpolation at Chebyshev nodes. Uniform\nconvergence and stability are proved in a couple of Holder - Zygmund spaces of\nlocally continuous functions. With respect to classical methods based on\nLagrange interpolation at the same collocation nodes, we succeed in reproducing\nthe optimal convergence rates of the L2 case by cutting off the typical log\nfactor which seemed inevitable dealing with uniform norms. Such an improvement\ndoes not require a greater computational effort. In particular we propose a\nfast algorithm based on the solution of a simple 2-bandwidth linear system and\nprove that, as its dimension tends to infinity, the sequence of the condition\nnumbers (in any natural matrix norm) tends to a finite limit.\n