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21: Bonita V. Saunders

… … ►Bonita V. Saunders, born in Portsmouth, Virginia, is a member of the Applied and Computational Mathematics Division of the Information Technology Laboratory at the National Institute of Standards and Technology. … ►Her research interests include numerical grid generation, numerical solution of partial differential equations, and visualization of special functions. …

22: Ronald F. Boisvert

… … ►His research interests include numerical solution of partial differential equations, mathematical software, and information services that support computational science. …

23: Howard S. Cohl

… … ► 1968 in Paterson, New Jersey) is a Mathematician in the Applied and Computational Mathematics Division at the National Institute of Standards and Technology in Gaithersburg, Maryland. … ►Cohl has published papers in orthogonal polynomials and special functions, and is particularly interested in fundamental solutions of linear partial differential equations on Riemannian manifolds, associated Legendre functions, generalized and basic hypergeometric functions, eigenfunction expansions of fundamental solutions in separable coordinate systems for linear partial differential equations, orthogonal polynomial generating function and generalized expansions, and $q$-series. …

24: 3.7 Ordinary Differential Equations

… ►For general information on solutions of equation (3.7.1) see §1.13. … ►

§3.7(ii) Taylor-Series Method: Initial-Value Problems

… ► … ►For $w^{\prime }=f(z,w)$ the standard fourth-order rule reads … ►For $w^{\prime \prime }=f(z,w,w^{\prime })$ the standard fourth-order rule reads …

25: Bibliography C

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Analytical solution of a model for complex food webs. Phys. Rev. E 65 (3), pp. (030901–1)–(030901–4).

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Referenced by:

§8.24(i).

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Three improvements in reduction and computation of elliptic integrals. J. Res. Nat. Inst. Standards Tech. 107 (5), pp. 413–418.

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External Links:

FullText

Referenced by:

§19.22(ii), §19.29(ii), §19.36(i), §19.8(i).

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Stationary solutions of the one-dimensional nonlinear Schrödinger equation. I. Case of repulsive nonlinearity. Phys. Rev. A 62 (063610), pp. 1–10.

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Referenced by:

§22.19(iii).

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Nonclassical Symmetry Reductions and Exact Solutions for Physically Significant Nonlinear Evolution Equations. In Nonlinear and Chaotic Phenomena in Plasmas, Solids and Fluids (Edmonton, AB, 1990), W. Rozmus and J. A. Tuszynski (Eds.), pp. 72–79.

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External Links:

MathReview

Referenced by:

§29.19(ii).

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Notes:

Complex interval standard function library. For details see Neher (2007)

External Links:

CoStLy

Referenced by:

§ ‣ Software Cross Index, M. Neher (2007).

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26: 1.13 Differential Equations

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§1.13(i) Existence of Solutions

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Fundamental Pair

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§1.13(v) Products of Solutions

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§1.13(vii) Closed-Form Solutions

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27: 28.33 Physical Applications

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Boundary-values problems arising from solution of the two-dimensional wave equation in elliptical coordinates. This yields a pair of equations of the form (28.2.1) and (28.20.1), and the appropriate solution of (28.2.1) is usually a periodic solution of integer order. See §28.33(ii).

… ►The wave equation …The general solution of the problem is a superposition of the separated solutions. … ►Substituting $z=\omega t$, $a=b/{\omega }^2$, and $2q=f/{\omega }^2$, we obtain Mathieu’s standard form (28.2.1). … ►However, in response to a small perturbation at least one solution may become unbounded. …

28: Barry I. Schneider

… … ►His current principal focus is developing novel methods for the solution of the time dependent Schrödinger equation in ultra-short, and intense laser fields. …

29: Frank W. J. Olver

… … ►He is particularly known for his extensive work in the study of the asymptotic solution of differential equations, i. …, the behavior of solutions as the independent variable, or some parameter, tends to infinity, and in the study of the particular solutions of differential equations known as special functions (e. …

30: Mathematical Introduction

… ►The NIST Handbook has essentially the same objective as the Handbook of Mathematical Functions that was issued in 1964 by the National Bureau of Standards as Number 55 in the NBS Applied Mathematics Series (AMS). … ►These include, for example, multivalued functions of complex variables, for which new definitions of branch points and principal values are supplied (§§1.10(vi), 4.2(i)); the Dirac delta (or delta function), which is introduced in a more readily comprehensible way for mathematicians (§1.17); numerically satisfactory solutions of differential and difference equations (§§2.7(iv), 2.9(i)); and numerical analysis for complex variables (Chapter 3). … ►With a few exceptions the adopted notations are the same as those in standard applied mathematics and physics literature. … ►His genius in the creation of the National Bureau of Standards Handbook of Mathematical Functions paid enormous dividends to the world’s scientific, mathematical, and engineering communities, and paved the way for the development of the NIST Handbook of Mathematical Functions and NIST Digital Library of Mathematical Functions. …