In this paper, we introduce two families of nontensorial generalised Hermite
polynomials/functions (GHPs/GHFs) in arbitrary dimensions, and develop efficient and …

The authors present a novel deep learning method for computing eigenvalues of the
fractional Schrödinger operator. The proposed approach combines a newly developed loss …

In this paper, we propose a sparse spectral-Galerkin approximation scheme for solving the
second-order partial differential equations on an arbitrary tetrahedron. Generalized …

We develop in this paper a high-order numerical method for fourth-order equation with
simply supported plate boundary conditions in a circular domain. By introducing an auxiliary …

It is widely recognized that numerical computation in high-dimensional problems poses a
significant challenge, particularly for intricate surface geometries, such as spherical and …

In this paper, we introduce two new families of generalised Hermite polynomials/functions
(GHPs/GHFs) in arbitrary dimensions, and develop efficient and accurate generalised …