Physics World

Neural networks discover unstable singularities in fluid systems

The Navier–Stokes partial differential equation was developed in the early 19th century by Claude-Louis Navier and George ...
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Non-linear mathematical techniques could lead to better flood forecasting

Although the world in which we live in is non-linear, or multi-dimensional, engineers and scientists have long used linear mathematical formulas to create models to predict physical phenomena such as ...
JSTOR Daily

Kinematic Geometry of Mass-Triangles and Reduction of Schrödinger's Equation of Three-Body Systems to Partial Differential Equations Solely Defined on Triangular Parameters

Proceedings of the National Academy of Sciences of the United States of America, Vol. 94, No. 17 (Aug. 19, 1997), pp. 8936-8938 (3 pages) ...
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Alternating direction implicit finite difference schemes for the Heston-Hull-White partial differential equation

In this paper we investigate the effectiveness of alternating direction implicit (ADI) time-discretization schemes in the numerical solution of the three-dimensional Heston-Hull-White partial ...
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Penalty methods for bilateral XVA pricing in European and American contingent claims by a partial differential equation model

Accounting for default risk in the valuation of financial derivatives has become increasingly important, especially since the 2007–8 financial crisis. Under some assumptions, the valuation of ...
JSTOR Daily

A Differential Games Solution to a Logarithmic Advertising Model

A logarithmic excess-advertising model of a duopoly is presented, and Nash optimal open-loop advertising strategies are determined. It turns out that if the two firms use different discount rates, ...