2025/10/20 by Bruno Degli Esposti, Esposti, Bruno Degli, Alessandra Sestini +1
Computer Science · Engineering · Mathematics · #FOS: Mathematics #Fractional Differential Equations Solutions #Numerical Analysis (math.NA) #Numerical methods in engineering #Numerical methods in inverse problems #cs.NA #math.NA
paper · pdf · doi:10.48550/arxiv.2510.17680
openalex publication_date 2025/10/20 · openalex created_date 2025/10/22 · arxiv created 2026/07/31 · openalex updated_date 2026/08/01 · arxiv updated 2026/08/03
The Nyström method for the numerical solution of Fredholm integral equations of the second kind is generalized by decoupling the set of solution nodes from the set of quadrature nodes. The accuracy and efficiency of the new method is investigated for smooth kernels and complex 2D domains using recently developed meshless moment-free quadrature formulas on scattered nodes. Compared to the classical Nyström method, our variant has a clear performance advantage, especially for narrow kernels. The decoupled Nyström method requires the choice of a reconstruction scheme to approximate values at quadrature nodes from values at solution nodes. We prove that, under natural assumptions, the overall order of convergence is the minimum between that of the quadrature scheme and of the reconstruction scheme. When the two schemes have the same order, we describe a simple procedure to determine experimentally a nearly optimal ratio between the densities of solution and quadrature nodes, for which our decoupled Nyström method achieves its maximum efficiency.