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 ...

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 paper presents a novel and direct approach to solving boundary- and final-value problems, corresponding to barrier options, using forward pathwise deep learning and forward–backward stochastic ...

An intermediate level course in the analytical and numerical study of ordinary differential equations, with an emphasis on their applications to the real world. Exact solution methods for ordinary ...

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 ...

Asymptotic error expansions have been obtained for certain numerical methods for linear Volterra integro-differential equations. These results permit the application ...

This course is available on the BSc in Business Mathematics and Statistics, BSc in Mathematics and Economics, BSc in Mathematics with Economics and BSc in Mathematics, Statistics and Business. This ...