Spectral methods are very efficient numerical algorithms for solving partial differential equations in relatively simple geometries. The numerical errors introduced by spectral algorithms typically ...

In this research field we are developing advanced computational methods centered around efficient solution strategies for partial differential equations. In numerical analysis, we focus on developing ...

Numerical analysis is the branch of mathematics devoted to the study of algorithms for the approximate solution of problems that often have no closed‐form answer. At its core, numerical analysis seeks ...

1 Introduction: Consequences of Numerical Inaccuracy 1 -- 1.1 Importance of Understanding Computational Statistics 1 -- 1.2 Brief History: Duhem to the Twenty-First Century 3 -- 1.3 Motivating Example ...

Due to the chaotic nature of the atmosphere, weather forecasts, even with ever improving numerical weather prediction models, eventually lose all skill. Meteorologists have a strong desire to better ...