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 ...

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 ...

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 ...

Studies properties and solutions of partial differential equations. Covers methods of characteristics, well-posedness, wave, heat and Laplace equations, Green's functions, and related integral ...

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 ...

A new technical paper titled “Solving sparse finite element problems on neuromorphic hardware” was published by researchers ...

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 ...

Field of expertise: Numerical analysis, machine learning and scientific computing Selected Projects • Mathematical Theory for Deep Learning It is the key goal of this project to provide a rigorous ...