A difference equation is used to model a problem that features a discrete time change. For example, to model the remaining debt of a loan which has a certain percentage of interest per month, we use ...

Moreover, research into elliptic differential-difference equations in the half-space has further illustrated how integral representations, such as Poisson-type formulae, can be used to establish ...

Overview Mathematics 376: Ordinary Differential Equations covers basic concepts, methods, and techniques for solving ordinary differential equations (ODEs) and considers applications of ODEs in ...

1 School of Mathematics and Computer Science, National University of Mongolia, Ulaanbaatar, Mongolia 2 School of Mathematics, Mongolian University of Science and Technology, Ulaanbaatar, Mongolia ...

The Loewner differential equation, introduced by Charles Loewner in 1923, describes the time evolution of a family of conformal (angle-preserving) functions defined on subsets of the complex plane.

By taking difference twice, we find that is a solution of Equation (1) for and that for and. Now, we put It is easy to see that is a solution of equation (8) for and is of type. The proof is complete.

G. A. Edgar, J. M. Rosenblatt, Difference Equations Over Locally Compact Abelian Groups, Transactions of the American Mathematical Society, Vol. 253 (Sep., 1979), pp ...

The solution by Womersley of the Navier-Stokes equations for fluid flow in distensible tubes has been most useful to students of hemodynamics. However, this solution requires linearization, and, ...