Paper:Billy Jackson/Partial dynamic equations on time scales

Billy Jackson: Partial dynamic equations on time scales

Published $2006$, Journal of Computational and Applied Mathematics.

Online copies

hosted by ScienceDirect

Contents

1. Introduction and motivation

Definition 1

2. Multivariable calculus on time scales

3. Partial differential operators

3.1 The homogeneous heat operator

Delta heat equation

3.1 The homogeneous wave operator

Delta wave equation

4. Nonhomogeneous operators

5. Mixed time scales

Appendix

Time scale

Real numbers

Quantum q greater than 1

Multiples of integers

Forward jump

Backward jump

Right scattered

Right dense

Left scattered

Left dense

Isolated point

Forward graininess