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Automatic Differentiation is Essential in Training Neural Networks for Solving Differential Equations. [PDF]

J Sci Comput
Chen C, Yang Y, Xiang Y, Hao W.
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Spectral shifted Chebyshev collocation technique with residual power series algorithm for time fractional problems. [PDF]

Sci Rep
Rida SZ, Arafa AAM, Hussein HS, Ameen IG, Mostafa MMM.   +4 more
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A novel method for approximate solution of two point non local fractional order coupled boundary value problems. [PDF]

PLoS One
Tadoummant L, Khalil H, Echarggaoui R, Aljohani S, Mlaiki N.   +4 more
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Spectral decoupling regulation through targeted ion migration in electro-optical resonators. [PDF]

Nat Commun
Li M, Li Y, Cong S, Zhang J, Li H, Zhang T, Hu D, Yong Z, Li Q, Wang Z, Zhao Z.   +10 more
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Solution of convection-diffusion model in groundwater pollution. [PDF]

Sci Rep
Rashidinia J, Momeni A, Molavi-Arabshahi M.   +2 more
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Influence of magnetic field-dependent viscosity on Casson-based nanofluid boundary layers: A comprehensive analysis using Lie group and spectral quasi-linearization method. [PDF]

Heliyon
Vishnu Ganesh N, Rajesh B, Al-Mdallal QM, Muzara H.   +3 more
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Rectangular spectral collocation

IMA Journal of Numerical Analysis, 2015
This work was supported by The MathWorks, Inc. and by King Abdullah University of Science and Technology (KAUST), award KUK-C1-013-04.
Driscoll, Tobin A., Hale, Nicholas
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Fractional Spectral Collocation Method

SIAM Journal on Scientific Computing, 2014
We develop an exponentially accurate fractional spectral collocation method for solving steady-state and time-dependent fractional PDEs (FPDEs). We first introduce a new family of interpolants, called fractional Lagrange interpolants, which satisfy the Kronecker delta property at collocation points.
Mohsen Zayernouri, George Em Karniadakis
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Spectral collocation methods for polymer brushes

The Journal of Chemical Physics, 2011
We provide an in-depth study of pseudo-spectral numerical methods associated with modeling the self-assembly of molten mixed polymer brushes in the framework of self-consistent field theory (SCFT). SCFT of molten polymer brushes has proved numerically challenging in the past because of sharp features that arise in the self-consistent pressure field at ...
Tanya L, Chantawansri, Su-Mi, Hur, Carlos J, García-Cervera, Hector D, Ceniceros, Glenn H, Fredrickson   +4 more
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