Heat transfer, encompassing conduction, convection, and radiation, is a fundamental physical process critical to engineering, environmental science, and materials development. Modeling heat transfer ...

Solving partial differential equations (PDEs) with numerical methods has a pivotal role in a wide variety of disciplines in science and engineering, with applications such as topology and design ...

Some lesser-known 3D printing simulation software with examples of implementation. Simulation is an essential tool in additive manufacturing (AM), with numerous options available from the largest ...

Nonlinear operators with long-distance spatiotemporal dependencies are fundamental in modelling complex systems across sciences; yet, learning these non-local operators remains challenging in machine ...

1 Department of Mathematics, Umm Al-Qura University, Mecca, Saudi Arabia. 2 Department of Mathematics, University College in Qunfudah, Umm Al-Qura University, Mecca, Saudi Arabia. Allen-Cahn equation ...

This contribution proposes two third-order numerical schemes for solving time-dependent linear and non-linear partial differential equations (PDEs). For spatial discretization, a compact fourth-order ...

Scientific computing increasingly requires both accurate simulations of physical systems as well as optimizing them over many parameters for tasks such as inverse ...