This repository allows you to solve forward and inverse problems related to partial differential equations (PDEs) using finite basis physics-informed neural networks (FBPINNs). To improve the ...
Learn how to solve differential equations using Euler and Runge-Kutta 4 methods! This tutorial compares both techniques, explaining accuracy, step size, and practical applications for physics and ...
SharpSMT first fuses DPLL(T) polytope enumeration with new factorization, variable-elimination and caching pre-processing, ...
Abstract: Inhomogeneous linear ordinary differential equations (ODEs) and systems of ODEs can be solved in a variety of ways. However, hardware circuits that can perform the efficient analog ...
Abstract: A set of two-dimensional (2D) electromagnetic (EM) MATLAB codes, using both first-order coupled differential (Maxwell) equations and second-order decoupled (wave) equations, are developed ...
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 ...
Creative Commons (CC): This is a Creative Commons license. Attribution (BY): Credit must be given to the creator. Population balance equation (PBE) models have the potential to automate many ...
Calculation: A representation of a network of electromagnetic waveguides (left) being used to solve Dirichlet boundary value problems. The coloured diagrams at right represent the normalized ...
Euler Method: The simplest numerical method for solving ODEs, which uses the derivative to project forward. [ y_{n+1} = y_n + h \cdot f(x_n, y_n) ] Heun's Method (Improved Euler Method): A two-step ...