This article presents the finite-difference time-domain (FDTD) method for gauge-invariant field-impulses, which constitute the fundamental physical quantities of electromagnetics (EM) in lieu of ...

Finite Difference Method (FDM): Implements numerical approximations for energy balance. Physics-Informed Neural Network (PINN): Integrates physical constraints into neural network training.

Fornberg, B. (1990) High-Order Finite Differences and the Pseudospectral Method on Staggered Grids. SIAM Journal on Numerical Analysis, 27, 904-918.

In this letter, a 2-D parameter-optimized spatial finite-difference temporal differential (SFDTD) method is presented, referred to as the PO-SFDTD method. First, the dispersion characteristic of the ...

Stable and accurate numerical solutions using the finite difference method (FDM) and finite element method (FEM) have been a major challenge to date as reported in a vast literature (Harari & Hughes ...

Toprakseven [17] derived a reliable finite difference method for fractional differential equations (FDEs) based on recently defined conformable fractional derivative. Li and Xu [18] constructed a time ...

In this paper, we investigate and analyze one-dimensional heat equation with appropriate initial and boundary condition using finite difference method. Finite difference method is a well-known ...

Elaborate management on bubble shape and transportations depends on the balance between multiple physical behaviors for two-phase flow with Marangoni stress and the interface mass transfer. In this ...