Nature

Numerical Solution of Differential and Integral Equations

Numerical methods for differential and integral equations are indispensable in modern applied mathematics and engineering, offering tools to approximate complex physical phenomena where analytical ...
JSTOR Daily

Efficient Solution of Nonlinear Ordinary Differential Equations Expressed in S-System Canonical Form

SIAM Journal on Numerical Analysis, Vol. 27, No. 3 (Jun., 1990), pp. 704-735 (32 pages) Ordinary differential equations can be recast into a nonlinear canonical form called an S-system. Evidence for ...
IEEE

Physics-guided Data Augmentation for Learning the Solution Operator of Linear Differential Equations

Abstract: Neural networks, especially the recent proposed neural operator models, are increasingly being used to find the solution operator of differential equations. Compared to traditional numerical ...
IEEE

Transmission Line Differential Protection Based on Numerical Solution of Partial Differential Equations

Abstract: Current differential protection is a widely adopted and effective high-voltage AC transmission line protection scheme. The long distance of the transmission line determines that the ...