Nature

Controllability of Parabolic Partial Differential Equations

Parabolic partial differential equations (PDEs) play a pivotal role in modelling processes that involve diffusion and thermal dynamics. Over recent decades, the study of their controllability – the ...
Nature

Error Analysis and Numerical Methods for Parabolic Partial Differential Equations

Parabolic partial differential equations (PDEs) are fundamental in modelling a wide range of diffusion processes in physics, finance and engineering. The numerical approximation of these equations ...
Risk

A reduced basis method for parabolic partial differential equations with parameter functions and application to option pricing

We consider the Heston model as an example of a parameterized parabolic partial differential equation. A space-time variational formulation is derived that allows for parameters in the coefficients ...
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 ...