Numerical Integration of Differential Equations and Large Linear Systems
Proceedings of two Workshops Held at the University of Bielefeld, Spring 1980
Published on 1. December 1982
Book
Paperback/Softback
VIII, 416 pages
978-3-540-11970-8 (ISBN)
Description
An overview of the techniques in use for solving the coupled equations of scattering theory.- Weyl's theory for second order differential equations and its application to some problems in quantum chemistry.- The discretization of continuous infinite sets of coupled ordinary linear differential equations: Application to the collision-induced dissociation of a diatomic molecule by an atom.- Extraction of continuum properties from L2 basis set matrix representations of the schr¿dinger equation: the sturm sequence polynomials and gauss quadrature.- Approximate solution of schr¿dinger's equation for atoms.- Numerical integration of linear inhomogeneous ordinary differential equations appearing in the nonadiabatic theory of small molecules.- Computation of solenoidal (divergence-free) vector fields.- Efficient solution of a nonlinear heat conduction problem by use of fast elliptic reduction and multigrid methods.- Are the numerical methods and software satisfactory for chemical kinetics?.- Optimization of nonlinear kinetic equation computation.- Automatic detection and treatment of oscillatory and/or stiff ordinary differential equations.- Characterization of non-linearly stable implicit Runge-Kutta methods.- Compact deferred correction formulas.- Solving odes in quasi steady state.- A singular perturbations approach to reduced-order modeling and decoupling for large scale linear systems.- Global codes for BVODEs and their comparison.- Global error estimation in ordinary initial value problems.- Lower bounds for the accuracy of linear multistep methods.- Asymptotic error expansions and discrete newton methods for elliptic boundary value problems.- The use of sparse matrix techniques in ode ¿ Codes.- On conjugate gradient methods for large sparse systems of linear equations.- A preconditioned tchebycheff iterative solution method for certain large sparse linear systems with a non-symmetric matrix.- On modified incomplete factorization methods.- Solving large sparse linear systems arising in queuing problems.- Large eigenvalue problems in quantum chemistry.- Variational pseudo-gradient method for determination of m first eigenstates of a large real symmetric matrix.- Simultaneous rayleigh-quotient iteration methods for large sparse generalized eigenvalue problems.- Large sparse unsymmetric eigenvalue problems.
More details
Series
Edition
1982 ed.
Language
English
Place of publication
Berlin
Germany
Publishing group
Springer Berlin
Target group
Professional and scholarly
Research
Illustrations
VIII, 416 p.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 23 mm
Weight
633 gr
ISBN-13
978-3-540-11970-8 (9783540119708)
DOI
10.1007/BFb0064877
Schweitzer Classification
Content
An overview of the techniques in use for solving the coupled equations of scattering theory.- Weyl's theory for second order differential equations and its application to some problems in quantum chemistry.- The discretization of continuous infinite sets of coupled ordinary linear differential equations: Application to the collision-induced dissociation of a diatomic molecule by an atom.- Extraction of continuum properties from L2 basis set matrix representations of the schrödinger equation: the sturm sequence polynomials and gauss quadrature.- Approximate solution of schrödinger's equation for atoms.- Numerical integration of linear inhomogeneous ordinary differential equations appearing in the nonadiabatic theory of small molecules.- Computation of solenoidal (divergence-free) vector fields.- Efficient solution of a nonlinear heat conduction problem by use of fast elliptic reduction and multigrid methods.- Are the numerical methods and software satisfactory for chemical kinetics?.- Optimization of nonlinear kinetic equation computation.- Automatic detection and treatment of oscillatory and/or stiff ordinary differential equations.- Characterization of non-linearly stable implicit Runge-Kutta methods.- Compact deferred correction formulas.- Solving odes in quasi steady state.- A singular perturbations approach to reduced-order modeling and decoupling for large scale linear systems.- Global codes for BVODEs and their comparison.- Global error estimation in ordinary initial value problems.- Lower bounds for the accuracy of linear multistep methods.- Asymptotic error expansions and discrete newton methods for elliptic boundary value problems.- The use of sparse matrix techniques in ode - Codes.- On conjugate gradient methods for large sparse systems of linearequations.- A preconditioned tchebycheff iterative solution method for certain large sparse linear systems with a non-symmetric matrix.- On modified incomplete factorization methods.- Solving large sparse linear systems arising in queuing problems.- Large eigenvalue problems in quantum chemistry.- Variational pseudo-gradient method for determination of m first eigenstates of a large real symmetric matrix.- Simultaneous rayleigh-quotient iteration methods for large sparse generalized eigenvalue problems.- Large sparse unsymmetric eigenvalue problems.