A mathematician at Carnegie Mellon University has developed an easier way to solve quadratic equations. The mathematician hopes this method will help students avoid memorizing obtuse formulas. His ...

Abstract: Based on deep neural network, elliptic partial differential equations in complex regions are solved. Accurate and effective strategies and numerical methods for elliptic partial differential ...

TensorFlow implementation for DAS-PINNs: A deep adaptive sampling method for solving high-dimensional partial differential equations. Physics-informed neural networks are a type of promising tools to ...

The codes developed in this repository are credited to all the members of the course NMPDE - Numerical Methods for Partial Differential Equations (2018) instructed by Prof. D. Palla, Dept. of ...

Abstract: In this article, a 3-D hybrid Maxwell’s equations finite-difference time-domain (ME-FDTD)/wave equation-based finite-element time-domain (WE-FETD) method is proposed. This method retains the ...

A mathematical brain teaser challenges people to solve the matchstick equation in just two moves. The puzzle uses matchsticks ...

The coordinates of the turning point and the equation of the line of symmetry can be found by writing the quadratic expression in completed square form. Find the equation of the line of symmetry and ...

Our purpose in this paper is to study the convergence rate of some variants of the Schwarz alternating method for solving two types of singularly perturbed advection-diffusion equations, one in which ...

Scientists are rethinking the universe’s deepest mysteries using numerical relativity, complex computer simulations of Einstein’s equations in extreme conditions. This method could help explore what ...

Biomedical Engineering combines biology and engineering to make technological breakthroughs in medical devices, procedures, and patient care. Biomedical engineers work in industries, in labs, and even ...