PHYSICSIn this article, we will explore the applications of linear ordinary differential equations (linear ODEs) in Physics and other branches of mathematics, and dig into the matrix method for solving linear ODEs. Although linear ODEs have a comparatively easy form, they are effective in solving ...
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of physics provided by differential equations, has been established and widely discussed in the literature. In general, PINN workflow incorporates the most fundamental and famous DNN configuration of Multilayer Perceptron (MLP). There also exist other types of algorithms in the class of deep learning...
On the integrability of linear and nonlinear partial differential equations A new method for studying boundary value problems for linear and for integrable nonlinear partial differential equations (PDE's) in two dimensions is revie... AS Fokas - 《Journal of Mathematical Physics》...
The formalism for linear absolute and convective instabilities developed in plasma physics (Briggs, 1964; Bers, 1973) is extended. The conclusion is that any order saddle point as well as any singular point of a frequency as a function o... Leonid,Brevdo - 《Geophysical & Astrophysical Fluid...
Neural networks can approximate the solution of differential equations15,16, in particular high-dimensional partial differential equations (PDEs)17,18. One of the most promising approaches to efficiently solve non-linear PDEs is physics-informed neural networks (PINNs)19,20,21. PINNs are trained to...
The numerical technique of differential quadrature for the solution of linear and non-linear partial differential equations, first introduced by Bellman an... SK Jang,CW Bert,AG Striz - 《International Journal for Numerical Methods in Engineering》 被引量: 147发表: 2010年 Nonconservative stability ...
Y Cao - 《Journal of Differential Equations》 被引量: 40发表: 2006年 A compact hamiltonian with the same asymptotic mean spectral density as the Riemann zeros For the classical hamiltonian (x + 1/x)(p + 1/p), with position x and conjugate momentum p, all orbits are bounded. After a ...
The corresponding reflection dip frequency as a function of the RI is shown in Fig. 4(b). The RI sensitivity S is about 1.94THz/RIU using the linear fitting for the reflection dip, and the FOM is about 506RIU−1, which is much larger than those of the other reported studies at THz...
In several practical applications, the dynamic processes that take place in a physical system are described using a set of partial differential equations (PDEs), which are typically nonlinear and coupled. The inverse problems that arise in those systems ought to be constrained to honour the ...