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Machine Learning: Science and TechnologyPhysics-informed neural networks (PINNs) are limited by three interlocking bottlenecks, the PINN trilemma : Monte-Carlo collocation, serial automatic differentiation, and a resulting stochastic loss landscape that prevents quasi-Newton optimisation ...
Conrard Giresse Tetsassi Feugmo +1 more
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, 2018 The study on spectral characteristics of biological soil crust in the water-wind erosion crisscross region in the Loess Plateau has important scientific value for the identification of biological soil crust based on remote sensing technology at regional ...
Sun, WY (reprint author), Northwest A&F Univ, State Key Lab Soil Eros & Dryland Farming Loess P, Yangling 712100, Shaanxi, Peoples R China. +7 more
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Construction of Fractional Pseudospectral Differentiation Matrices with Applications
AxiomsDifferentiation matrices are an important tool in the implementation of the spectral collocation method to solve various types of problems involving differential operators.
Wenbin Li, Hongjun Ma, Tinggang Zhao
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International Journal of Differential Equations, 2012 A numerical scheme is presented for a class of time fractional differential equations with Dirichlet's and Neumann's boundary conditions. The model solution is discretized in time and space with a spectral expansion of Lagrange interpolation polynomial ...
Fenghui Huang
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Accelerate the Electrolyte Perturbed-Chain Statistical Associating Fluid Theory-Density Functional Theory Calculation With the Chebyshev Pseudo-Spectral Collocation Method. Part II. Spherical Geometry and Anderson Mixing. [PDF]
Front Chem, 2021 Sun Y +5 more
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Collocation methods for a class of second order initial value problems with oscillatory solutions [PDF]
, 1993 We derive and analyse two families of multistep collocation methods for periodic initial-value problems of the form y" = f(x, y); y((^x)o) = yo, y(^1)(xo) = zo involving ordinary differential equations of second order in which the first derivative ...
Booth, Andrew S.
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Fractal and FractionalIn this paper, we have established a numerical method for a class of time-fractional and Riesz space distributed-order advection–diffusion equation with time-delay.
Fang Wang, Yuxue Chen, Yuting Liu
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Space-time spectral methods for PDEs on irregular domains
Spectral methods are used to solve partial differential equations numerically. When the solution is analytic, the rate of convergence of the numerical solution is exponential; that is, the error decays exponentially.
Wilegoda Liyanage, Chandramali Piyasundara
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Abstract and Applied Analysis, 2014 We present a numerical method for a class of boundary value problems on the unit interval which feature a type of power-law nonlinearity. In order to numerically solve this type of nonlinear boundary value problems, we construct a kind of spectral ...
A. H. Bhrawy +2 more
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Spectral collocation methods in solid mechanics
, 2022 Spectral collocation methods are advertised as a powerful tool for a numerical so- lution of boundary value problems for ordinary as well as partial differential equations.
Trnka, Ladislav
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