AI techniques excel at solving complex equations in physics, especially inverse problems

Differential equations are fundamental tools in physics: they are used to describe phenomena ranging from fluid dynamics to general relativity. But when these equations become stiff (i.e. they involve ...
Nature

Analytical Methods in Differential Systems and Vector Fields

Analytical methods in differential systems and vector fields combine classical techniques with modern computational approaches to elucidate the intricate dynamics of nonlinear systems. Researchers use ...
JSTOR Daily

Alternating Direction Implicit Orthogonal Spline Collocation Methods for an Evolution Equation with a Positive-Type Memory Term

SIAM Journal on Numerical Analysis, Vol. 46, No. 1 (2007/2008), pp. 344-364 (21 pages) New numerical techniques are presented for the solution of a class of linear partial integro-differential ...
JSTOR Daily

Closed-Form Solutions of the Nonlinear Partial Differential Equations Governing the Stress-Field in a Rigid, Perfectly-Plastic Body

In this paper closed-form solutions for the evaluation of the stress-field in a rigid perfectly-plastic body under plane-stress or plane-strain conditions are estimated. The two nonlinear partial ...
Risk

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 ...