Phase-change materials (PCMs) are important photonic materials that have the advantages
of a rapid and reversible phase change, a great difference in the optical properties between …

In this paper, we discuss a Stefan problem that includes a moving phase change material
and a size-dependent thermal conductivity. This model also includes the time-dependent …

Phase-changing materials are nowadays getting global attention on account of their ability
to store excess energy. Solar thermal energy can be stored in phase changing material …

By the iteration of the theta-formula and treating the neighbors explicitly such as the
unconditionally positive finite difference (UPFD) methods, we construct a new 2-stage …

We examine the one-dimensional transient diffusion equation with a space-dependent
diffusion coefficient. Such equations can be derived from the Fokker–Planck equation and …

The improved element-free Galerkin (IEFG) method is proposed in this paper for solving 3D
Helmholtz equations. The improved moving least-squares (IMLS) approximation is used to …

Calculating heat transfer in building components is an important and nontrivial task. Thus, in
this work, we extensively examined 13 numerical methods to solve the linear heat …

Abstract Physics-Informed Neural Networks (PINNs) are artificial neural networks that
encode Partial Differential Equations (PDEs) as an integral component of the ML model …

The removal of vapor molecules from a droplet surface is an important stage of evaporation
in a vapor–gas mixture. In this work, with the evaporation of a water droplet in a vapor–gas …

In this work, a modified form of Taylor series is proposed which we call the moving Taylor
series. We prove theorems that formulate coefficients of the proposed series along with the …