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 ...

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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 ...

Studies properties and solutions of partial differential equations. Covers methods of characteristics, well-posedness, wave, heat and Laplace equations, Green's functions, and related integral ...

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 ...

We present efficient partial differential equation (PDE) methods for continuous-time mean-variance portfolio allocation problems when the underlying risky asset follows a stochastic volatility process ...