Nature

Fuzzy Differential Equations and Their Applications

Fuzzy differential equations (FDEs) extend classical differential equations by incorporating uncertainty through fuzzy numbers. This mathematical framework is particularly valuable for modelling ...
JSTOR Daily

On the Selection of Ordinary Differential Equation Models with Application to Predator-Prey Dynamical Models

We consider model selection and estimation in a context where there are competing ordinary differential equation (ODE) models, and all the models are special cases of a "full" model. We propose a ...
JSTOR Daily

Kolmogorov Equations in Infinite Dimensions: Well-Posedness and Regularity of Solutions, with Applications to Stochastic Generalized Burgers Equations

The Annals of Probability, Vol. 34, No. 2 (Mar., 2006), pp. 663-727 (65 pages) We develop a new method to uniquely solve a large class of heat equations, so-called Kolmogorov equations in infinitely ...
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 ...
Nature

Delay Differential Equations and Their Applications

Delay differential equations (DDEs) extend classical ordinary differential equations by incorporating dependencies on past states. This inclusion of time delays is critical for accurately modelling ...