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Numerical Integration of Differential Equations and Large Linear Systems (Lecture Notes in Mathematics) - Softcover
Synopsis
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 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 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 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.
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