Showing papers on "L-stability published in 1993"
TL;DR: A parallel implementation of implicit Runge–Kutta methods with real eigenvalues and a method for estimating the local error and an implementation of these methods on parallel machines are proposed.
16 citations
TL;DR: An iteration scheme to tackle the numerical integration of a stiff ordinary differential equation by means of a suitable choice of the iteration parameters, the implicit relations for the stage values can be uncoupled so that they can be solved in parallel.
15 citations
TL;DR: Popular methods for the integration of a stiff initial-value problem for a system of ordinary differential equations (ODEs) require the solution of systems of linear equations, but it is shown that the matrices are very ill-conditioned.
12 citations
TL;DR: This article incorporates three iterative methods for solving nonsymmetric linear systems of equations in DASSL, which is a program for numerical integration of systems of stiff ODEs and Differential-Algebraic Equations (DAEs).
5 citations
TL;DR: In this paper, a two-integration-formulas shooting method for the solution of ordinary boundary value problems is presented, where the state equations are integrated using a higher order formula, whereas a lower order formula is used for the variational equations.
5 citations
DOI•
01 Jan 1993
TL;DR: In this paper, Runge-Kutta methods were applied to stiff systems in singular perturbation form to give accurate approximations of phase portraits near hyperbolic stationary points.
Abstract: Runge–Kutta methods applied to stiff systems in singular perturbation form are shown to give accurate approximations of phase portraits near hyperbolic stationary points. Over arbitrarily long time intervals, Runge–Kutta solutions shadow solutions of the differential equation and vice versa. Precise error bounds are derived. The proof uses attractive invariant manifolds to reduce the problem to the nonstiff case, which was previously studied by Beyn.
3 citations
01 Sep 1993
2 citations
01 Apr 1993
TL;DR: In this article, an effective method of numerically integrating such large, stiff systems of equations is proposed to minimize the size of the system of equations that need to be solved simultaneously, a steady-state approximation of some variables and partition into subsystems is adopted, incorporating the information about the eigenvalues of the linearized equations and qualitative physical information.
Abstract: The dynamic behavior of a chemical plant containing a large number of process variables with different response speeds is characterized by linearized ordinary differential equations with eigenvalues of widely varying magnitudes. An effective method of numerically integrating such large, stiff systems of equations is proposed. To minimize the size of the system of equations that need to be solved simultaneously, a steady-state approximation of some variables and partition into subsystems is adopted, incorporating the information about the eigenvalues of the linearized equations and qualitative physical information about the model. The eigenvalues are recalculated to reconfirm the validity of these two methods of reducing the number of dimensions. The proposed method is applied to a fuel-cell power plant with 31 ordinary differential equations, with an effective dynamic simulation being able to be performed.
1 citations
01 Jan 1993
TL;DR: In this article, a class of equations which can be solved by quadratures is considered, and a quadrature can be used to solve the third and higher order differential equations.
Abstract: Here ordinary differential equations of third and higher order are considered; in particular, a class of equations which can be solved by quadratures is exploited.
01 Jan 1993
TL;DR: In this article, a method of finding analytical solutions to the class of nonlinear ordinary differential equations given by ============\/\/\/\/\/\/££€£££/$££$££ £€£ £ ££ £££
Abstract: In this paper we present a method of finding analytical solutions to the class of nonlinear ordinary differential equations given by
$$ {f^{{''}}} + A(f){f^{'}} + B(f){\left( {{f^{'}}} \right)^2} + C(f) = 0 $$
. These types of equations appear frequently in mathematical physics and its applications to the physics of many-body problems. Except for very special cases, little is known about their analytical solutions.
TL;DR: In this paper, a class of perturbed collocation schemes for stiff boundary value problems in systems of first-order ordinary differential equations is presented. But the perturbation term has to be a non-rational function of the stiffness matrix of the problem.