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 ...

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 ...