Neuromorphic computers, inspired by the architecture of the human brain, are proving surprisingly adept at solving complex ...

Masaki Kashiwara has won the 2025 Abel prize, sometimes called the Nobel prize of mathematics, for his work on algebraic analysis. Kashiwara, a professor at Kyoto University, Japan, received the award ...

Adequate mathematical modeling is the key to success for many real-world projects in engineering, medicine, and other applied areas. Once a well-suited model is established, it can be thoroughly ...

Abstract: This paper introduces Physics-Informed Deep Equilibrium Models (PIDEQs) for solving initial value problems (IVPs) of ordinary differential equations (ODEs). Leveraging recent advancements in ...

ABSTRACT: This study compares the Adomian Decomposition Method (ADM) and the Variational Iteration Method (VIM) for solving nonlinear differential equations in engineering. Differential equations are ...

This project demonstrates the use of finite difference methods to solve Laplace's and Maxwell's equations using MATLAB. It includes a 2D solver for potential distribution and a 1D FDTD simulation for ...

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

The paper aims to utilize an integral transform, specifically the Khalouta transform, an abstraction of various integral transforms, to address fractional differential equations using both ...

Abstract: This paper introduces two novel methods for solving multi-order fractional differential equations using Bernstein polynomials. The first method, referred to as the fractional operational ...