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: In this paper, the active control problem for thermoacoustic instability in the Rijke tube is investigated. First of all, the first-order hyperbolic partial differential equations (PDEs) for ...

A few years ago, every time he visited his hometown, Tung got drunk and sat on the river bank looking over the water towards his ex-girlfriend’s house. There he remembered the times when they were ...

Numerical Relativity is a multidisciplinary field including relativity, magneto-hydrodynamics, astrophysics and computational methods, among others, with the aim of solving numerically ...

More than 70 years ago, researchers at the forefront of artificial intelligence research introduced neural networks as a revolutionary way to think about how the brain works. In the human brain, ...

Nonlinear differential equations appear in many domains and are notoriously difficult to solve. Whereas previous quantum algorithms for general nonlinear differential equations have complexity ...

These attempts would never solve my problem outright, but they might garner evidence toward an answer. My lack of programming expertise and resulting impatience slowed the process, making it an ...

Partial differential equations (PDEs) are among the most ubiquitous tools used in modeling problems in nature. However, solving high-dimensional PDEs has been notoriously difficult due to the “curse ...

In this paper, we originate results with finite difference schemes to approximate the solution of the classical Fisher Kolmogorov Petrovsky Piscounov (KPP) equation from population dynamics. Fisher’s ...

In this work, we present final solving Millennium Prize Problems formulated by Clay Math. Inst., Cambridge. A new uniform time estimation of the Cauchy problem solution for the Navier-Stokes equations ...