3 Hermite spectral scheme for the logistic model This section is for application of the Hermite spectral approximation to the Logistic equation in two-dimensions. We construct a Hermite spectral ...

Learning data-driven discretizations for partial differential equations Code associated with the paper: Learning data-driven discretizations for partial differential equations. Yohai Bar-Sinai, ...

In this paper, an optimization framework of partial differential neural network combined with divide-space sampling (PDNN-DSS) is proposed to solve the estimation and control problem of 3D ...

Course content The course provides an introduction to the theoretical basis for linear partial differential equations, focusing on elliptic equations and eigenvalue problems. The techniques and ...

Article citations More>> Anane, A., Chakrone, O. and Moradi, N. (2006) Maximum and Anti-Maximum Principles for the Laplacian with a Nonlinear Boundary Condition. Electronic Journal of Differential ...

Multi-language suite for high-performance solvers of differential equations and scientific machine learning (SciML) components. Ordinary differential equations (ODEs), stochastic differential ...

The nonlinear Schrödinger equation (NLSE) is a fundamental equation in quantum mechanics with applications in optical fibers, plasma physics, and biomolecule dynamics. The focus of this paper is on ...