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 ...

Course on using spectral methods to solve partial differential equations. We will cover the exponential convergence of spectral methods for periodic and non-periodic problem, and a general framework ...

This issue of The Journal of Computational Finance has numerical partial differential equation discretization techniques as its central theme. Modern aspects like ...

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 ...

Direct modeling for computational fluid dynamics provides an effective methodology to develop multi-scale numerical algorithms for flow simulation in all regimes from rarefied to continuum ones, which ...

Real numbers, limits, continuity, differentiability, mean-value theorems, Taylor's theorem with remainders, indeterminate forms, maxima and minima, asyptotes ...