Wolfgang R. Wasow

Bio: Wolfgang R. Wasow is an academic researcher. The author has contributed to research in topics: Stochastic partial differential equation & Finite difference method. The author has an hindex of 9, co-authored 9 publications receiving 3959 citations.

Asymptotic expansions for ordinary differential equations

Abstract: Asymptotic expansions for ordinary differential equations , Asymptotic expansions for ordinary differential equations , مرکز فناوری اطلاعات و اطلاع رسانی کشاورزی

Linear turning point theory

Abstract: I Historical Introduction.- 1.1. Early Asymptotic Theory Without Turning Points.- 1.2. Total Reflection and Turning Points.- 1.3. Hydrodynamic Stability and Turning Points.- 1.4. The So-Called WKB Method.- 1.5. The Contribution of R. E. Langer.- 1.6. Remarks on Recent Trends.- II Formal Solutions.- 2.1. Introduction.- 2.2. The Jordan Form of Holomorphic Functions.- 2.3. A Formal Block Diagonalization.- 2.4. Parameter Shearing: Its Nature and Purpose.- 2.5. Simplification by a Theorem of Arnold.- 2.6. Parameter Shearing: Its Application.- 2.7. Parameter Shearing: The Exceptional Case.- 2.8. Formal Solution of the Differential Equation.- 2.9. Some Comments and Warnings.- III Solutions Away From Turning Points.- 3.1. Asymptotic Power Series: Definition of Turning Points.- 3.2. A Method for Proving the Analytic Validity of Formal.- Solutions: Preliminaries.- 3.3. A General Theorem on the Analytic Validity of Formal.- Solutions.- 3.4. A Local Asymptotic Validity Theorem.- 3.5. Remarks on Points That Are Not Asymptotically Simple.- IV Asymptotic Transformations of Differential Equations.- 4.1. Asymptotic Equivalence.- 4.2. Formal Invariants.- 4.3. Formal Circuit Relations with Respect to the Parameter.- V Uniform Transformations at Turning Points: Formal Theory.- 5.1. Preparatory Simplifications.- 5.2. A Method for Formal Simplification in Neighborhoods of a Turning Point.- 5.3. The Case h > 1.- 5.4. The General Theory for n = 2.- VI Uniform Transformations at Turning Points: Analytic Theory.- 6.1. Preliminary General Results.- 6.2. Differential Equations Reducible to Airy's Equation.- 6.3. Differential Equations Reducible to Weber's Equation.- 6.4. Uniform Transformations in a Full Neighborhood of.- a Turning Point.- 6.5. Complete Reduction to Airy's Equation.- 6.6. Reduction to Weber's Equation in Wider Sectors.- 6.7. Reduction to Weber's Equation in a Full Disk.- VII Extensions of the Regions of Validity of the Asymptotic Solutions.- 7.1. Introduction.- 7.2. Regions of Asymptotic Validity Bounded by Separation Curves: The Problem.- 7.3. Solutions Asymptotically Known in Sectors Bounded by.- Separation Curves.- 7.4. Singularities of Formal Solutions at a Turning Point.- 7.5. Asymptotic Expansions in Growing Domains.- 7.6. Asymptotic Solutions in Expanding Regions: A General Theorem.- 7.7. Asymptotic Solutions in Expanding Regions: A Local Theorem.- VIII Connection Problems.- 8.1. Introduction.- 8.2. Stretching and Parameter Shearing.- 8.3. Calculation of the Restraint Index.- 8.4. Inner and Outer Solutions for a Particular nth-Order System.- 8.5. Calculation of a Central Connection Matrix.- 8.6. Connection Formulas Calculated Through Uniform Simplification.- IX Fedoryuk's Global Theory of Second-Order Equations.- 9.1. Global Formal Solutions of ?2u"=a(x)u2u" = a(x)u.- 9.2. Separation Curves for ?2u"=a(x)u2u" = a(x)u.- 9.3. A Global Asymptotic Existence Theorem for ?2u"=a(x)u2u" = a(x)u.- X Doubly Asymptotic Expansions.- 10.1. Introduction.- 10.2. Formal Solutions for Large Values of the.- Independent Variable.- 10.3. Asymptotic Solutions for Large Values of the.- Independent Variable.- 10.4. Some Properties of Doubly Asymptotic Solutions.- 10.5. Central Connection Problems in Unbounded Regions.- XI A Singularly Perturbed Turning Point Problem.- 11.1. The Problem.- 11.2. A Simple Example.- 11.3. The General Case: Formal Part.- 11.4. The General Case: Analytic Part.- XII Appendix: Some Linear Algebra for Holomorphic Matrices.- 12.1. Vectors and Matrices of Holomorphic Functions.- 12.2. Reduction to Jordan Form.- 12.3. General Holomorphic Block Diagonalization.- 12.4. Holomorphic Transformation of Matrices into Arnold's Form.- References.

Analytic Combinatorics

Abstract: Analytic Combinatorics is a self-contained treatment of the mathematics underlying the analysis of discrete structures, which has emerged over the past several decades as an essential tool in the understanding of properties of computer programs and scientific models with applications in physics, biology and chemistry. Thorough treatment of a large number of classical applications is an essential aspect of the presentation. Written by the leaders in the field of analytic combinatorics, this text is certain to become the definitive reference on the topic. The text is complemented with exercises, examples, appendices and notes to aid understanding therefore, it can be used as the basis for an advanced undergraduate or a graduate course on the subject, or for self-study.

Enhancements of the simple method for predicting incompressible fluid flows

Abstract: Variations of the SIMPLE method of Patankar and Spalding have been widely used over the past decade to obtain numerical solutions to problems involving incompressible flows. The present paper shows several modifications to the method which both simplify its implementation and reduce solution costs. The performances of SIMPLE, SIMPLER, and SIMPLEC (the present method) are compared for two recirculating flow problems. The paper is addressed to readers who already have experience with SIMPLE or its variants.

Dynamic Equations on Time Scales: An Introduction with Applications

Abstract: Preface * The Time Scales Calculus * First Order Linear Equations * Second Order Linear Equations * Self-Adjoint Equations * Linear Systems and Higher Order Equations * Dynamic Inequalities * Linear Symplectic Dynamic Systems * Extensions * Solutions to Selected Problems * Bibliography * Index

A flexible inversion algorithm for retrieval of aerosol optical properties from Sun and sky radiance measurements

Abstract: The problem of deriving a complete set of aerosol optical properties from Sun and sky radiance measurements is discussed. Algorithm development is focused on improving aerosol retrievals by means of including a detailed statistical optimization of the influence of noise in the inversion procedure. The methodological aspects of such an optimization are discussed in detail and revised according to both modern findings in inversion theory and practical experience in remote sensing. Accordingly, the proposed inversion algorithm is built on the principles of statistical estimation: the spectral radiances and various a priori constraints on aerosol characteristics are considered as multisource data that are known with predetermined accuracy. The inversion is designed as a search for the best fit of all input data by a theoretical model that takes into account the different levels of accuracy of the fitted data. The algorithm allows a choice of normal or lognormal noise assumptions. The multivariable fitting is implemented by a stable numerical procedure combining matrix inversion and univariant relaxation. The theoretical inversion scheme has been realized in the advanced algorithm retrieving aerosol size distribution together with complex refractive index from the spectral measurements of direct and diffuse radiation. The aerosol particles are modeled as homogeneous spheres. The atmospheric radiative transfer modeling is implemented with well-established publicly available radiative transfer codes. The retrieved refractive indices can be wavelength dependent; however, the extended smoothness constraints are applied to its spectral dependence (and indirectly through smoothness constraints on retrieved size distributions). The positive effects of statistical optimization on the retrieval results as well as the importance of applying a priori constraints are discussed in detail for the retrieval of both aerosol size distribution and complex refractive index. The developed algorithm is adapted for the retrieval of aerosol properties from measurements made by ground-based Sun-sky scanning radiometers used in the Aerosol Robotic Network (AERONET). The results of numerical tests together with examples of experimental data inversions are presented.

A steepest descent method for oscillatory Riemann–Hilbert problems. Asymptotics for the MKdV equation

Abstract: In this article we present a new and general approach to analyzing the asymptotics of oscillatory Riemann-Hilbert problems. Such problems arise, in particular, when evaluating the long-time behavior of nonlinear wave equations solvable by the inverse scattering method. We will restrict ourselves here exclusively to the modified Korteweg-de Vries (MKdV) equation