Partial differential equations (PDE) describe the behavior of fluids, structures, heat transfer, wave propagation, and other physical phenomena of scientific and engineering interest. This course ...

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

Finite element methods (FEM) constitute a foundational numerical approach for solving partial differential equations by discretising complex domains into smaller, manageable subdomains known as ...

Discontinuous Galerkin (DG) methods represent a versatile and robust class of numerical schemes for approximating solutions to partial differential equations (PDEs). Combining elements of finite ...

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 ...

The Sinc-Galerkin method originally proposed by Stenger is extended to handle fourth-order ordinary differential equations. The exponential convergence rate of the method, $\mathcal{O}(e^{-\kappa\sqrt ...

An intermediate level course in the analytical and numerical study of ordinary differential equations, with an emphasis on their applications to the real world. Exact solution methods for ordinary ...