Numerical Analysis 2000 Vol. VI: Ordinary Differential Equations and Integral Equations

North-Holland.: Elsevier, 2003. — (xviii+540) p. English. (OCR-слой).[From: Journal of Computational and Applied Mathematics (2000) Volume 125, Issues 1-2, Pages 1-540 (15 December 2000)].This volume contains contributions in the area of differential equations and integral equations. The editors wish to thank the numerous authors, referees, and fellow editors Claude Brezinski and Luc Wuytack, who have made this volume a possibility; it has been a major but personally rewarding effort to compile it. Due to the limited number of pages we were obliged to make a selection when composing this volume. At an early stage it was agreed that, despite the connections between the subject areas, it would be bene cial to allocate the area of partial differential equations to a volume for that area alone.
Many numerical methods have arisen in response to the need to solve "real-life" problems in
applied mathematics, in particular problems that do not have a closed-form solution. It is particularly relevant to this comment that our Journal title involves the expression "Computational and Applied Mathematics". Applied mathematicians from differing academic cultures display differing approaches to computational techniques, but one might hazard the prophecy, based on current observations, that future generations of applied mathematicians will (without necessarily sacri cing mathematical rigour) almost universallyregard the use of, and possibly the analysis and design of, robust numerical algorithms as an essential part of their research activity.J.C. Butcher. Numerical methods for ordinary differential equations in the 20th century.
L.F. Shampine and Robert M. Corless. Initial value problems for ODEs in problem solving environments.
N. Borovykh and M.N. Spijker. Resolvent conditions and bounds on the powers of matrices, with relevance to numerical stability of initial value problems.
W. Govaerts. Numerical bifurcation analysis for ODEs.
Arieh Iserles and Antonella Zanna. Preserving algebraic invariants with Runge–Kutta methods.
V. Antohe and I. Gladwell. Performance of two methods for solving separable Hamiltonian systems.
Ernst Hairer and Gerhard Wanner. Order stars and stiff integrators.
G.Vanden Berghe, H.De Meyer, M.Van Daele and T.Van Hecke. Exponentially fitted Runge–Kutta methods.
J.R. Cash. Modified extended backward differentiation formulae for the numerical solution of stiff initial value problems in ODEs and DAEs.
Shengtai Li and Linda Petzold. Software and algorithms for sensitivity analysisof large-scale differential algebraic systems.
John T. Betts, Neil Biehn, Stephen L. Campbell and William P. Huffman. Compensating for order variation in mesh refinement for direct transcription methods.
W.H. Enright. Continuous numerical methods for ODEs with defect control.
Kevin Burrage, Pamela Burrage and Taketomo Mitsui. Numerical solutions of stochastic differential equations – implementation and stability issues.
Gennadii A. Bocharov and Fathalla A. Rihan. Numerical modelling in biosciences using delay differential equations.
John Norbury and R. Eddie Wilson. Dynamics of constrained differential delay equations.
Christopher T.H. Baker. A perspective on the numerical treatment of Volterra equations.
Alfredo Bellen, Nicola Guglielmi and Marino Zennaro. Numerical stability of nonlinear delay differential equations of neutral type.
Koen Engelborghs, Tatyana Luzyanina and Dirk Roose. Numerical bifurcation analysis of delay differential equations.
Neville J. Ford and Volker Wulf. How do numerical methods perform for delay differential equations undergoing a Hopf bifurcation?
Christopher A.H. Paul. Designing efficient software for solving delay differential equations.
Evelyn Buckwar. Introduction to the numerical analysis ofstochastic delay differential equations.
Christopher T.H. Baker. Retarded differential equations.
Simon Shaw and J.R. Whiteman. Adaptive space–time finite element solution for Volterra equations arising in viscoelasticity problems.
L.Gr. Ixaru. CP methods for the Schrödinger equation.
Alan L. Andrew. Asymptotic correction of Numerov's eigenvalueestimates with natural boundary conditions.
Leon Greenberg and Marco Marletta. Numerical methods for higher order Sturm–Liouville problems.
B.M. Brown, D.K.R. McCormack and A. Zettl. On a computer assisted proof of the existence of eigenvalues below the essential spectrum of the Sturm–Liouville problem.
Peter Junghanns and Bernd Silbermann. Numerical analysis for one-dimensional Cauchy singular integral equations.
J. Elschner and I.G. Graham. Numerical methods for integral equations of Mellin type.
A. Rathsfeld. Quadrature methods for 2D and 3D problems.
Ian H. Sloan. Qualocation.
W. Hackbusch and B.N. Khoromskij. A sparse-matrix arithmetic: general complexity estimates.
Ernst P. Stephan. Multilevel methods for the h-, p-, and hp-versions of the boundary element method.
G.C. Hsiao, O. Steinbach and W.L. Wendland. Domain decomposition methods via boundary integral equations.
Author Index Volume 125 (2000).