Oscillation theory concerns the study of qualitative behaviour of solutions to differential equations, with particular focus on the presence or absence of infinitely many sign changes over unbounded ...

Sometimes, it’s easy for a computer to predict the future. Simple phenomena, such as how sap flows down a tree trunk, are straightforward and can be captured in a few lines of code using what ...

Whether it's physical phenomena, share prices or climate models—many dynamic processes in our world can be described mathematically with the aid of partial differential equations. Thanks to ...

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 ...

Time-domain finite-difference (TDFD) method is the most dominant approach for seismic wavefield simulation. Due to the memory and computational cost of the computer, finite-difference (FD) simulations ...

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 ...