Numerical solutions of partial differential equations enable a broad range of scientific
research. The Dedalus project is a flexible, open-source, parallelized computational …

Approximation Theory and Approximation Practice (“ATAP”), originally published in 2013,
concerns approximation of nonperiodic functions on the interval [− 1, 1], the Chebyshev …

In this paper we present a new approach to solve the fuel-efficient powered descent
guidance problem on large planetary bodies with no atmosphere (eg, Moon or Mars) using …

A spectral method for solving linear partial differential equations (PDEs) with variable
coefficients and general boundary conditions defined on rectangular domains is described …

The first step when solving an infinite-dimensional eigenvalue problem is often to discretize
it. We show that one must be extremely careful when discretizing nonlinear eigenvalue …

In swimming microorganisms and the cell cytoskeleton, inextensible fibers resist bending
and twisting, and interact with the surrounding fluid to cause or resist large-scale fluid …

Every animal cell is filled with a cytoskeleton, a dynamic gel made of inextensible fibers,
such as microtubules, actin fibers, and intermediate filaments, all suspended in a viscous …

We introduce a fast direct solver for variable-coefficient elliptic PDEs on surfaces based on
the hierarchical Poincaré–Steklov method. The method takes as input an unstructured, high …

What if all you had to do to solve an ODE were just to write it down? 1 That is the line we will
follow in this book. Our emphasis is not just on the mathematics of ODEs, but on how the …

We provide an optimal growth spatio-temporal setting with capital accumulation and
diffusion across space to study the link between economic growth triggered by capital spatio …