This paper presents a new approach to spectral methods for initial boundary value problems. A filtered version of the partial differential equation and the initial and boundary conditions at an ...

Far-from-equilibrium dynamics controls a broad range of processes in nature and technology, from celestial events to atoms.

Singularly perturbed systems of ordinary differential equations are considered for which the reduced problem has an infinite family of solutions. Recent approaches to such problems are compared, and a ...

Reviews ordinary differential equations, including solutions by Fourier series. Physical derivation of the classical linear partial differential equations (heat, wave, and Laplace equations). Solution ...