Embedded boundary conditions in spectral methods: A rectangular matrix approach

O. Guimarães and José R.C. Piqueira

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 241, issue PB, 225-237

Abstract: Boundary conditions play a crucial role in determining well-posed solutions to differential equations. This paper introduces an innovative spectral method framework in Hilbert spaces that systematically embeds boundary conditions directly into the differential operator structure. Through the construction of modified operators ℒδ (where δ denotes the highest derivative order), our approach streamlines numerical solutions while maintaining spectral accuracy, particularly benefiting high-order equations (δ>2).

Keywords: Spectral methods; Operational matrices; Hilbert spaces; Orthogonal bases; Error estimation; Eigenvalues problems (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:241:y:2026:i:pb:p:225-237

DOI: 10.1016/j.matcom.2025.10.001

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