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 ...

Computer scientists have devised an innovative and elegantly concise algorithm that can efficiently solve systems of linear equations that are critical to such important computer applications as image ...

Liouville's formula for certain class of linear operator equations of order n is derived. The result is applied to solving a linear second order operator equation. A number of examples which ...

Description: First order quasi-linear equations and their application to physical and social sciences; the Cauchy-Kovalevsky theorem; characteristics, classification, and canonical form of linear ...

Two essential quantities for the analysis of approximation schemes of evolution equations are stability and convergence. We derive stability and convergence of fully discrete approximation schemes of ...

This paper investigates the existence of solutions for nonlinear fractional differential equations with integral boundary conditions on an unbounded domain. An example illustrating how the theory can ...