Determining optical flow

Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes

https://www.uio.no/studier/emner/matnat/astro/AST5110/h12/undervisningsmateriale/van-leer1979.pdf

Towards the ultimate conservative difference scheme V. A second-order sequel to Godunov's method

Preface 1. Introduction 2. Conservation laws and differential equations 3. Characteristics and Riemann problems for linear hyperbolic equations 4. Finite-volume methods 5. Introduction to the CLAWPACK software 6. High resolution methods 7. Boundary conditions and ghost cells 8. Convergence, accuracy, and stability 9. Variable-coefficient linear equations 10. Other approaches to high resolution 11. Nonlinear scalar conservation laws 12. Finite-volume methods for nonlinear scalar conservation laws 13. Nonlinear systems of conservation laws 14. Gas dynamics and the Euler equations 15. Finite-volume methods for nonlinear systems 16. Some nonclassical hyperbolic problems 17. Source terms and balance laws 18. Multidimensional hyperbolic problems 19. Multidimensional numerical methods 20. Multidimensional scalar equations 21. Multidimensional systems 22. Elastic waves 23. Finite-volume methods on quadrilateral grids Bibliography Index.

https://depts.washington.edu/clawpack/book2/sample.pdf

Finite Volume Methods for Hyperbolic Problems

The instructor's manual to a work which introduces the fundamental principles of meteorology, explaining storm dynamics and the dynamics of climate and its global implications.

An introduction to dynamic meteorology

Difference Methods for Initial-Value Problems.

. We study some variants of the Erdős similarity problem. We pose the question if every measurable subset of the real line with positive measure contains a similar copy of an inﬁnite geometric progression. We construct a compact subset 𝐸 of the real line such that 0 is a Lebesgue density point of 𝐸 , but 𝐸 does not contain any (non-constant) inﬁnite geometric progression. We give a suﬃcient density type condition that guarantees that a set contains an inﬁnite geometric progression. By slightly improving a recent result of Bradford, Kohut and Mooroogen [1], we construct a closed set 𝐹 ⊂ [ 0 , ∞) such that the measure of 𝐹 ∩[ 𝑡,𝑡 + 1 ] tends to 1 at inﬁnity but 𝐹 does not contain any inﬁnite arithmetic progression. We also slightly improve a more general recent result by Kolountzakis and Papageorgiou [2] for more general sequences. WegiveasuﬃcientconditionthatguaranteesthatagivenCantortypesetcontains at least one inﬁnite geometric progression with any quotient between 0 and 1. This can be applied to most symmetric Cantor sets of positive measure.

Samuel Goldberg

Papers

Difference Methods for Initial-Value Problems.

Large sets avoiding infinite arithmetic / geometric progressions

Mathematics and Statistics for Economists.