Numerical Boundary Value ODEs Proceedings of an International Workshop, Vancouver, Canada, July 10–13, 1984 / by Ascher, Russell.

In the past few years, knowledge about methods for the numerical solution of two-point boundary value problems has increased significantly. Important theoretical and practical advances have been made in a number or fronts, although they are not adequately described in any tt'xt currently availa...

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Bibliographic Details
Main Authors: Ascher (Author), Russell (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser, 1985.
Edition:1st ed. 1985.
Series:Progress in Scientific Computing ; 5
Springer eBook Collection.
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Online Access:Click to view e-book
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Table of Contents:
  • I. Conditioning, dichotomy and related numerical considerations
  • A unified view of some recent developments in the numerical solution of BVODEs
  • The role of conditioning in shooting techniques
  • On non-invertible boundary value problems
  • Riccati transformations: When and how to use?
  • Discretizations with dichotomic stability for two-point boundary value problems
  • II. Implementation aspects of various methods
  • Improving the performance of numerical methods for two-point boundary value problems
  • Reducing the number of variational equations in the implementation of multiple shooting
  • The spline-collocation and the spline-Galerkin methods for Orr-Sommerfeld problem
  • III. Singular perturbation (‘stiff’) problems
  • On the simultaneous use of asymptotic and numerical methods to solve nonlinear two-points problems with boundary and interior layers
  • Two families of symmetric difference schemes for singular perturbation problems
  • A numerical method for singular perturbation problems with turning points
  • Numerical solution of singular perturbed boundary value problems using a collocation method with tension splines
  • IV. Bifurcation problems and delay differential equations
  • Solving boundary value problems for functional differential equations by collocation
  • The approximation of simple singularities
  • Calculating the loss of stability by transient methods, with application to parabolic partial differential equations
  • A Runge-Kutta-Nystrom method for delay differential equations
  • V. Special applications
  • A finite difference method for the basic stationary semiconductor device equations
  • Solution of premixed and counterflow diffusion flame problems by adaptive boundary value methods.