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 ...

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 ...

Many dynamic processes can be described mathematically with the aid of stochastic partial differential equations. Scientists have found a new method which helps to solve a certain class of such ...

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 ...

Karl J. Havlak, Harold Dean Victory, Jr. We devise and study a random particle method for approximating Vlasov-Poisson-Fokker-Planck systems. Such a proposed scheme takes into account the fact that ...

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 ...

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