The very large theory of difference equations in the field of analytic functions of a complex variable has been completely omitted.

SIAM Journal on Numerical Analysis, Vol. 51, No. 4 (2013), pp. 2470-2490 (21 pages) The primary aim of this paper is to answer the question, What are the highest-order five-or nine-point compact ...

Let T denote a subset of the possible transitions between the states of a finite Markov chain and let Yk denote the time of the kth occurrence of a T-transition. Formulae are derived for the ...

Computing derivatives by finite-difference approximations can be very time consuming, especially for second-order derivatives based only on values of the objective function (FD= option). If analytical ...

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

Peter Austing shows how to set up finite difference solvers to exactly recover the prices of all vanilla options on the grid. The approach leads to a specific discretisation of Dupire’s formula. It ...

Physics and Python stuff. Most of the videos here are either adapted from class lectures or solving physics problems. I really like to use numerical calculations without all the fancy programming ...