Fourier analysis and numerical methods have long played a pivotal role in the solution of differential equations across science and engineering. By decomposing complex functions into sums of ...

In this paper we study numerical methods to approximate the adapted solutions to a class of forward-backward stochastic differential equations (FBSDE's). The almost sure uniform convergence as well as ...

An important characterization of a numerical method for first order ODE's is the region of absolute stability. If all eigenvalues of the linear problem y' = Ay are inside this region, the numerical ...

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

Ordinary differential equations (ODEs) are also called initial value problems because a time zero value for each first-order differential equation is needed. The following is an example of a ...

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 ...