Ordinary differential equations (ODEs) and difference equations serve as complementary tools in the mathematical modelling of processes evolving in continuous and discrete time respectively. Together ...

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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 ...

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 ...

In this paper, we consider the numerical valuation of swing options in electricity markets based on a two-factor model. These kinds of contracts are modeled as path dependent options with multiple ...