Difference equations, serving as the discrete analogue to differential equations, have long been a linchpin in the study of dynamic systems. These equations define sequences recursively, and their ...

Ordinary differential equations (ODEs) and difference equations serve as complementary tools in the mathematical modelling of processes evolving in continuous and discrete time respectively. Together ...

A homogeneous linear difference equation with constant coefficients over a locally compact abelian group $G$ is an equation of the form $\sum^n_{j=1} c_jf (t_jx) = 0 ...

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 ...

An intermediate level course in the analytical and numerical study of ordinary differential equations, with an emphasis on their applications to the real world. Exact solution methods for ordinary ...

We all know how differential equations are a crucial part of engineering design and analysis. We have some powerful software tools for this today. Well, here is what led up to our modern analysis ...