Fourth-order elliptic equations, often characterised by the inclusion of the biharmonic operator (Δ²), play a pivotal role in the mathematical modelling of complex physical systems. They arise in ...

A simple invariant characterization of the scalar fourth-order ordinary differential equations which admit a variational multiplier is given. The necessary and sufficient conditions for the existence ...

The Sinc-Galerkin method originally proposed by Stenger is extended to handle fourth-order ordinary differential equations. The exponential convergence rate of the method, $\mathcal{O}(e^{-\kappa\sqrt ...

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 ...