Parabolic partial differential equations (PDEs) are fundamental in modelling a wide range of diffusion processes in physics, finance and engineering. The numerical approximation of these equations ...

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 ...

Linearization methods have been used in the numerical analysis of finite element solutions to nonlinear partial differential equations (PDEs) for quite a long time. Frequently, essential properties ...

Backward stochastic differential equations (BSDEs) have emerged as a pivotal mathematical tool in the analysis of complex systems across finance, physics and engineering. Their formulation, generally ...

This is a preview. Log in through your library . Abstract Spline collocation methods are proposed for the spatial discretization of a class of hyperbolic partial integro-differential equations arising ...

We present efficient partial differential equation (PDE) methods for continuous-time mean-variance portfolio allocation problems when the underlying risky asset follows a stochastic volatility process ...

We propose a new numerical approach to solving high-dimensional partial differential equations (PDEs) that arise in the valuation of exotic derivative securities. The proposed method is extended from ...

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 ...

A new technical paper titled “Solving sparse finite element problems on neuromorphic hardware” was published by researchers at Sandia National Lab. Abstract “The finite element method (FEM) is one of ...