The mGFD (meshless Generalized Finite Differences) repository provides a comprehensive solution for numerically solving Partial Differential Equations in two dimensions on highly irregular regions.

Computational fluid dynamics (CFD) is a branch of physics that utilizes numerical methods and algorithms to analyze and predict the behavior of fluids and gases under various conditions. This field ...

Compared to the conventional high-order staggered-grid finite-difference method (C-SFD), the time–space domain dispersion-relation-based high-order staggered-grid finite-difference method (TS-SFD) can ...

A new study by Shanghai Jiao Tong University and SII Generative AI Research Lab (GAIR) shows that training large language models (LLMs) for complex, autonomous tasks does not require massive datasets.

Abstract: This letter proposes a generalized and controllable-stability conformal method to address stability challenges inherent in conformal finite-difference time-domain algorithms. A quantitative ...

The finite element method is a powerful numerical technique that is used in all major engineering industries - in this video we'll explore how it works. We'll look at why it's useful to split the body ...

ABSTRACT: Fractional-order time-delay differential equations can describe many complex physical phenomena with memory or delay effects, which are widely used in the fields of cell biology, control ...

Abstract: 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 ...

All the codes are distributed under MIT License on GitHub and are free to use, modify, and distribute giving the proper copyright notice. This repository proposes a way to achieve approximations to ...

A novel stochastic numerical scheme is introduced to solve stochastic differential equations. The development of the scheme is based on two different parts. One part finds the solution for the ...