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 ...

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

Finite element methods (FEM) have emerged as a versatile and robust framework for the numerical simulation of evolving partial differential equations (PDEs). These methods discretise complex ...

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

This paper develops two local mesh-free methods for designing stencil weights and spatial discretization, respectively, for parabolic partial differential equations (PDEs) of ...

This is a preview. Log in through your library . Abstract An original method of integration is described for quasi-linear hyperbolic equations in three independent variables. The solution is ...

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 ...

We propose a hybrid spatial finite-difference/pseudospectral discretization for European option-pricing problems under the Heston and Heston–Hull–White models. In ...