Overdetermined problems in the context of elliptic partial differential equations concern boundary‐value formulations in which more conditions are prescribed than are generally required for a unique ...

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 ...

Nonlinear eigenvalue problems arise when one seeks pairs (λ,u) satisfying an equation of the form F(λ,u)=0 in a function space, subject to boundary or decay conditions. In contrast to linear spectral ...

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 ...