Jacobi rational operational approach for time-fractional sub-diffusion equation on a semi-infinite domain

RM Hafez, YH Youssri, AG Atta - Contemporary Mathematics, 2023 - ojs.wiserpub.com
… Applying the proper transformations may be used to let Jacobi polynomials suitable in the
numerical solution of differential equations on semi-infinite domains. One typical method for …

Exponential convergence of deep operator networks for elliptic partial differential equations

C Marcati, C Schwab - SIAM Journal on Numerical Analysis, 2023 - SIAM
… in the numerical solution of differential equations in science and engineering. We refer the
reader to the survey [2] for uses and successes of DNN based numerical … some operations on …

Numerical solution of time-fractional telegraph equations using wavelet transform

M Mulimani - International Journal of Dynamics and Control, 2024 - Springer
… The operational matrices of integration are extracted from the Taylor wavelets. The Taylor
wavelet method (TWM) is developed using these operational integration matrices. According …

Projective synchronization for uncertain fractional reaction-diffusion systems via adaptive sliding mode control based on finite-time scheme

Y Kao, C Wang, H Xia, Y Cao - … and Control for Fractional-order Systems, 2024 - Springer
… In this chapter, the projective synchronization of uncertain fractional-order reaction-diffusion
systems is studied for the first time via the fractional adaptive sliding mode control method. …

PhyCRNet: Physics-informed convolutional-recurrent network for solving spatiotemporal PDEs

P Ren, C Rao, Y Liu, JX Wang, H Sun - … Methods in Applied Mechanics and …, 2022 - Elsevier
… Hence, we consider pixel shuffle operation as a preferable upsampling strategy in the … the
numerical solution of the Burgers’ equations for 1000 time steps within the duration of [ 0 , 2 ] . …

On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks

S Wang, H Wang, P Perdikaris - … Methods in Applied Mechanics and …, 2021 - Elsevier
Using this analysis, we propose a family of novel architectures that can effectively mitigate
spectral bias and enable the solution of problems for which current PINN approaches fail. …

Transistors based on two-dimensional materials for future integrated circuits

S Das, A Sebastian, E Pop, CJ McClellan… - Nature …, 2021 - nature.com
… of 2D field-effect transistors for use in future VLSI technologies. We consider the key performance
indicators for aggressively scaled 2D … during high-current operation. Several measures …

A Legendre-spectral method for Hadamard fractional partial differential equations

G Istafa, M ur Rehman - Mathematical Sciences, 2024 - Springer
method to obtain numerical solutions of Caputo–Hadamard fractional partial differential
equations. For … Legendre polynomials to establish a procedure based on operational matrices of …

Two-dimensional MXenes for electrochemical capacitor applications: Progress, challenges and perspectives

Q Zhu, J Li, P Simon, B Xu - Energy Storage Materials, 2021 - Elsevier
… of MXenes, but only about a small number have been prepared and used for capacitive
energy storage applications (supercapacitors) so far, with Ti 3 C 2 T x being the most studied one…

Weak SINDy for partial differential equations

DA Messenger, DM Bortz - Journal of Computational Physics, 2021 - Elsevier
method Variational System Identification (VSI) is introduced to identify reaction-diffusion
systems and uses … WSINDy is a method for discovering PDEs without the use of any pointwise …