Covers finite difference, finite element, finite volume, pseudo-spectral, and spectral methods for elliptic, parabolic, and hyperbolic partial differential equations. Prereq., APPM 5600. Recommended ...

Continuation of APPM 5470. Advanced study of the properties and solutions of elliptic, parabolic, and hyperbolic partial differential equations. Topics include the study of Sobolev spaces and ...

Linear and quasilinear first order PDE. The method of characteristics. Conservation laws and propagation of shocks. Basic theory for three classical equations of mathematical physics (in all spatial ...

Course on using spectral methods to solve partial differential equations. We will cover the exponential convergence of spectral methods for periodic and non-periodic problem, and a general framework ...

SIAM Journal on Numerical Analysis, Vol. 50, No. 6 (2012), pp. 3351-3374 (24 pages) In this paper quasi-Monte Carlo (QMC) methods are applied to a class of elliptic partial differential equations ...

HERNÁN R. HENRÍQUEZ, EDUARDO HERNÁNDEZ M. In this paper we establish the existence of mild solutions for a class of abstract second-order partial neutral functional differential equations with ...

Calculation: A representation of a network of electromagnetic waveguides (left) being used to solve Dirichlet boundary value problems. The coloured diagrams at right represent the normalized ...

A new proof marks major progress toward solving the Kakeya conjecture, a deceptively simple question that underpins a tower of conjectures. Computer Proof ‘Blows Up’ Centuries-Old Fluid Equations For ...