Abstract.The subject of this paper is the analytic approximation of solution to stochastic differential delay equations with Poisson jump. We introduce approximate methods for stochastic differential ...

We describe an Euler scheme to approximate solutions of Lévy driven stochastic differential equations (SDEs) where the grid points are given by the arrival times of a Poisson process and thus are ...

Calculation: A representation of a network of electromagnetic waveguides (left) being used to solve Dirichlet boundary value problems. The coloured diagrams at right represent the normalized ...

Two new approaches allow deep neural networks to solve entire families of partial differential equations, making it easier to model complicated systems and to do so orders of magnitude faster. In high ...

Harmonic functions, defined as twice continuously differentiable functions satisfying Laplace’s equation, have long been a subject of intense study in both pure and applied mathematics. Their ...