Solving boundary value problems via the Nyström method using spline Gauss rules Hashemian, Ali Sliusarenko, Hanna Remogna, Sara Barrera Rosillo, Domingo Bartoň, Michael Artículo publicado recientemente. Dos años de embargo. We propose to use spline Gauss quadrature rules for solving boundary value problems (BVPs) using the Nyström method. When solving BVPs, one converts the corresponding partial differential equation inside a domain into the Fredholm integral equation of the second kind on the boundary in the sense of boundary integral equation (BIE). The Fredholm integral equation is then solved using the Nyström method, which involves the use of a particular quadrature rule, thus, converting the BIE problem to a linear system. We demonstrate this concept on the 2D Laplace problem over domains with smooth boundary as well as domains containing corners. We validate our approach on benchmark examples and the results indicate that, for a fixed number of quadrature points (i.e., the same computational effort), the spline Gauss quadratures return an approximation that is by one to two orders of magnitude more accurate compared to the solution obtained by traditional polynomial Gauss counterparts. 2024-01-30T11:12:01Z 2024-01-30T11:12:01Z 2023-08-01 journal article Ali Hashemian, Hanna Sliusarenko, Sara Remogna, Domingo Barrera, Michael Bartoň, Solving boundary value problems via the Nyström method using spline Gauss rules, Computers & Mathematics with Applications 143 (2023) 33-47, https://doi.org/10.1016/j.camwa.2023.04.035 https://hdl.handle.net/10481/87627 10.1016/j.camwa.2023.04.035 eng embargoed access Elsevier