Stable Spectral Methods for Time-Dependent Problems and the Preservation of Structure
Sign Up to like & getrecommendations! Published in 2024 at "Foundations of Computational Mathematics"
DOI: 10.1007/s10208-024-09647-w
Abstract: This paper is concerned with orthonormal systems in real intervals, given with zero Dirichlet boundary conditions. More specifically, our interest is in systems with a skew-symmetric differentiation matrix (this excludes orthonormal polynomials). We consider a… read more here.
Keywords: time dependent; spectral methods; function; methods time ... See more keywords
Learning unbounded-domain spatiotemporal differential equations using adaptive spectral methods
Sign Up to like & getrecommendations! Published in 2024 at "Journal of Applied Mathematics and Computing"
DOI: 10.1007/s12190-024-02131-2
Abstract: Rapidly developing machine learning methods have stimulated research interest in computationally reconstructing differential equations (DEs) from observational data, providing insight into the underlying mechanistic models. In this paper, we propose a new neural-ODE-based method that… read more here.
Keywords: differential equations; unbounded domain; spectral methods; domain spatiotemporal ... See more keywords
Fractional pseudo-spectral methods for distributed-order fractional PDEs
Sign Up to like & getrecommendations! Published in 2018 at "International Journal of Computer Mathematics"
DOI: 10.1080/00207160.2017.1421949
Abstract: ABSTRACT We develop a pseudo-spectral method of Petrov–Galerkin sense, employing nodal expansions in the weak formulation of distributed-order fractional partial differential equations. We define the underlying distributed Sobolev spaces and the associated norms. Then, we… read more here.
Keywords: pseudo spectral; distributed order; order; spectral methods ... See more keywords
Spectral methods for coupled channels with a mass gap
Sign Up to like & getrecommendations! Published in 2018 at "Physical Review D"
DOI: 10.1103/physrevd.97.036017
Abstract: CITATION: Weigel, H., Quandt, M. & Quandt, M. 2018. Spectral methods for coupled channels with a mass gap. Physical Review D, 97(3):036017, doi:10.1103/PhysRevD.97.036017. read more here.
Keywords: channels mass; spectral methods; coupled channels; methods coupled ... See more keywords
Sensitivity of Pansharpening Methods to Temporal and Instrumental Changes Between Multispectral and Panchromatic Data Sets
Sign Up to like & getrecommendations! Published in 2017 at "IEEE Transactions on Geoscience and Remote Sensing"
DOI: 10.1109/tgrs.2016.2606324
Abstract: In this work, the authors investigate the behaviors of the two main classes of pansharpening methods: those based on component substitution (CS) or spectral methods and those based on multiresolution analysis (MRA) or spatial methods,… read more here.
Keywords: data sets; pansharpening methods; spectral methods; pan ... See more keywords
Application of Spectral Methods to Inverse Dynamic Problem of Seismicity of a Stratified Medium
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Applied and Industrial Mathematics"
DOI: 10.1134/s1990478918040142
Abstract: Under study is the wave propagation process in the half-space y3 = 0 with the Cartesian coordinates y1, y2, and y3 which is filled with an elastic medium. The parameters of the medium are discontinuous… read more here.
Keywords: application spectral; methods inverse; dynamic problem; inverse dynamic ... See more keywords
Spectral Methods in Nonlinear Optics Equations for Non-Uniform Grids Using an Accelerated NFFT Scheme
Sign Up to like & getrecommendations! Published in 2022 at "Symmetry"
DOI: 10.3390/sym15010047
Abstract: In this work, we propose the use of non-homogeneous grids in 1D and 2D for the study of various nonlinear physical equations using spectral methods. As is well known, the use of spectral methods allow… read more here.
Keywords: optics equations; nonlinear optics; optics; non uniform ... See more keywords