Risk

Numerical simulation and applications of the convection–diffusion–reaction equation with the radial basis function in a finite-difference mode

This paper develops two local mesh-free methods for designing stencil weights and spatial discretization, respectively, for parabolic partial differential equations (PDEs) of ...
JSTOR Daily

Numerical Solution of Stochastic Differential Equations with Constant Diffusion Coefficients

Mathematics of Computation, Vol. 49, No. 180 (Oct., 1987), pp. 523-542 (20 pages) We present Runge-Kutta methods of high accuracy for stochastic differential ...
University of Bristol

Solution to century-old math problem could predict transmission of infectious diseases

The analytic solution of the diffusion equation in finite domains, when time and space is continuous, has been known for a long time. “However, to compare model predictions with empirical observations ...
Risk

Efficient numerical valuation of European options under the two-asset Kou jump-diffusion model

This paper concerns the numerical solution of the two-dimensional time-dependent partial integro-differential equation that holds for the values of European-style options under the two-asset Kou ...

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 ...