Differential equations are fundamental tools in physics: they are used to describe phenomena ranging from fluid dynamics to general relativity. But when these equations become stiff (i.e. they involve ...

Humans have been solving problems since the beginning of time. Our problem-solving skills are responsible for spurring social and technological advancement. However, over time, our individual skills ...

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 ...

The team has improved the capabilities of physics-informed neural networks (PINNs), a type of artificial intelligence that incorporates physical laws into the learning process. Researchers from the ...

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 ...

In this article, we have presented a novel and unified numerical strategy for addressing the Benjamin-Bona-Mahony (BBM) type partial differential equations with the use of the Fibonacci wavelets and ...

Most famous equation: Einstein's E = mc2, which means energy is equal to mass times the speed of light squared. Known digits of pi: More than 105 trillion digits Digits of pi NASA uses for equations: ...

For many of us, mathematics in school was a subject that not only demanded endless practice but also caused anxiety before exams. However, when it comes to brain teasers, the experience is quite ...