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 ...

General aspects of polynomial interpolation theory. Formulations in different basis, e.g. Lagrange, Newton etc. and their approximation and computational properties ...

Root mean square error (rms, or its square, the variance distance) is often used to measure differences between simulated and observed fields. In this case ...

SIAM Journal on Numerical Analysis, Vol. 53, No. 3 (2015), pp. 1585-1607 (23 pages) The diffraction grating problem is modeled by a boundary value problem governed by ...

We propose a new concept which allows us to apply any numerical method of weak approximation to a very broad class of stochastic differential equations (SDEs) with nonglobally Lipschitz coefficients.

Due to the chaotic nature of the atmosphere, weather forecasts, even with ever improving numerical weather prediction models, eventually lose all skill. Meteorologists have a strong desire to better ...