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

Partial Differential Equations (PDEs) are mathematical equations that involve unknown multivariate functions and their partial derivatives. They are the cornerstone of modelling a vast array of ...

Introductory course on using a range of finite-difference methods to solve initial-value and initial-boundary-value problems involving partial differential equations. The course covers theoretical ...

SIAM Journal on Numerical Analysis, Vol. 5, No. 3 (Sep., 1968), pp. 530-558 (29 pages) A new iterative method has been developed for solving the large sets of algebraic equations that arise in the ...

SIAM Journal on Numerical Analysis, Vol. 46, No. 5 (2008), pp. 2411-2442 (32 pages) This work proposes and analyzes an anisotropic sparse grid stochastic collocation method for solving partial ...

In this paper we investigate the effectiveness of alternating direction implicit (ADI) time-discretization schemes in the numerical solution of the three-dimensional Heston-Hull-White partial ...