Numerical methods for differential and integral equations are indispensable in modern applied mathematics and engineering, offering tools to approximate complex physical phenomena where analytical ...

The reasons a class of codes for solving ordinary differential equations might want to use an extremely small step size are investigated. For this class the likelihood of precision difficulties is ...

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 ...

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 ...

Partial differential equations can describe everything from planetary motion to plate tectonics, but they’re notoriously hard to solve. Unless you’re a physicist or an engineer, there really isn’t ...