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 present paper may be considered as a sequel to our previous paper in the Proceedings of the Cambridge Philosophical Society, Theorie generale de noyaux reproduisants-Premiere partie (vol 39 (1944)) which was written in 1942-1943 In the introduction to this paper we outlined the plan of papers which were to follow In the meantime, however, the general theory has been developed in many directions, and our original plans have had to be changed Due to wartime conditions we were not able, at the time of writing the first paper, to take into account all the earlier investigations which, although sometimes of quite a different character, were, nevertheless, related to our subject Our investigation is concerned with kernels of a special type which have been used under different names and in different ways in many domains of mathematical research We shall therefore begin our present paper with a short historical introduction in which we shall attempt to indicate the different manners in which these kernels have been used by various investigators, and to clarify the terminology We shall also discuss the more important trends of the application of these kernels without attempting, however, a complete bibliography of the subject matter (KAR) P 2

/pdf/theory-of-reproducing-kernels-2rpdlfjhn3.pdf

Theory of Reproducing Kernels.

/pdf/asymptotic-analysis-of-periodic-structures-14wjonu4ba.pdf

Asymptotic Analysis of Periodic Structures

* Measure Theory-Basic Notions * Measure Theory-Key Results * Processes, Distributions, and Independence * Random Sequences, Series, and Averages * Characteristic Functions and Classical Limit Theorems * Conditioning and Disintegration * Martingales and Optional Times * Markov Processes and Discrete-Time Chains * Random Walks and Renewal Theory * Stationary Processes and Ergodic Theory * Special Notions of Symmetry and Invariance * Poisson and Pure Jump-Type Markov Processes * Gaussian Processes and Brownian Motion * Skorohod Embedding and Invariance Principles * Independent Increments and Infinite Divisibility * Convergence of Random Processes, Measures, and Sets * Stochastic Integrals and Quadratic Variation * Continuous Martingales and Brownian Motion * Feller Processes and Semigroups * Ergodic Properties of Markov Processes * Stochastic Differential Equations and Martingale Problems * Local Time, Excursions, and Additive Functionals * One-Dimensional SDEs and Diffusions * Connections with PDEs and Potential Theory * Predictability, Compensation, and Excessive Functions * Semimartingales and General Stochastic Integration * Large Deviations * Appendix 1: Advanced Measure Theory * Appendix 2: Some Special Spaces * Historical and Bibliographical Notes * Bibliography * Indices

http://cyber.sibsutis.ru:82/Monarev/docs/nauka/PROBABILITY/Kallenberg%20O.%20Foundations%20of%20Modern%20Probability%20(Springer,1997)(ISBN%200387949577)(535s).pdf

Foundations of modern probability

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Über die partiellen Differenzengleichungen der mathematischen Physik

Keywords: ecoulement : compressible ; ecoulement : supersonique ; onde de : choc Reference Record created on 2005-11-18, modified on 2016-08-08

Supersonic flow and shock waves

Problems involving the classical linear partial differential equations of mathematical physics can be reduced to algebraic ones of a very much simpler structure by replacing the differentials by difference quotients on some (say rectilinear) mesh. This paper will undertake an elementary discussion of these algebraic problems, in particular of the behavior of the solution as the mesh width tends to zero. For present purposes we limit ourselves mainly to simple but typical cases, and treat them in such a way that the applicability of the method to more general difference equations and to those with arbitrarily many independent variables is made clear.

On the partial difference equations of mathematical physics

We discuss first-order systems of nonlinear conservation laws which have as a consequence an additional conservation law. We show that if the additional conserved quantity is a convex function of the original ones, the original system can be put into symmetric hyperbolic form. Next we derive an entropy inequality, which has also been suggested by I. Kružhkov, for discontinuous solutions of the given system of conservation laws.

https://www.pnas.org/content/pnas/68/8/1686.full.pdf

Kurt Friedrichs

Papers

Über die partiellen Differenzengleichungen der mathematischen Physik

Supersonic flow and shock waves

On the partial difference equations of mathematical physics

Systems of Conservation Equations with a Convex Extension

Symmetric positive linear differential equations