A simple NSC-RKHS algorithm for solving linear boundary value problems -- Error bounds and implementations

DOI10.1016/j.amc.2012.04.062zbMath1280.65073OpenAlexW2026427304MaRDI QIDQ387473

Grzegorz Andrzejczak

Publication date: 23 December 2013

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2012.04.062

zbMATH Keywords

Sobolev spaceserror boundsreproducing kernellinear boundary value problemsnormal spline collocation method

Mathematics Subject Classification ID

Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Error bounds for numerical methods for ordinary differential equations (65L70) Linear boundary value problems for ordinary differential equations (34B05)

Related Items (3)

Spline reproducing kernels on \(\mathbb{R}\) and error bounds for piecewise smooth LBV problems ⋮ Fast variants of the NSC-RKHS algorithm for solving linear boundary value problems ⋮ Reproducing kernel method for the numerical solution of the Brinkman-Forchheimer momentum equation

Cites Work

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• A new algorithm for a class of linear nonlocal boundary value problems based on the reproducing kernel method
• Uniqueness of solutions of linear nonlocal boundary value problems
• A numerical algorithm for solving a class of linear nonlocal boundary value problems
• A new reproducing kernel Hilbert space method for solving nonlinear fourth-order boundary value problems
• Solving singular two-point boundary value problem in reproducing kernel space
• Representation of the exact solution for infinite system of linear equations
• The method of normal spline collocation
• Theoretical Numerical Analysis
• Theory of Reproducing Kernels

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