Journal ArticleDOI
Determining Initial Values for Stiff Systems of Ordinary Differential Equations
TLDR
In this article, the authors consider a stiff system of nonlinear ordinary differential equations for which we know some but not all of the initial conditions and present an algorithm which determines the unknown initial values in such a way that the solution does not have an initial transient.Abstract:
We consider a stiff system of nonlinear ordinary differential equations for which we know some but not all of the initial conditions. This paper presents an algorithm which determines the unknown initial values in such a way that the solution does not have an initial transient. The algorithm was motivated by a problem from tonospheric physics in which two of the initial conditions are unknown. By physical considerations, the correct solution should not have an initial transient. This requirement allows us to uniquely specify the two unknown initial values.read more
Citations
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Journal ArticleDOI
Numerical solution of the atmospheric diffusion equation for chemically reacting flows
TL;DR: A comprehensive study of numerical techniques for solving the atmospheric diffusion equation is reported in this article, in which the three-dimensional problem is converted into a sequence of one-dimensional problems, and a Galerkin, linear finite element scheme with a nonlinear filter is found to be computationally superior to other methods tested for the advection-diffusion components.
Journal ArticleDOI
Plasma transport in the auroral return current region
TL;DR: In this paper, the classical and anomalous transport properties of a multifluid plasma consisting of H(+, O(+), and electron populations in the presence of auroral field-aligned return currents are investigated, using a multimoment fluid model with anomalous transfer coefficients.
Journal ArticleDOI
Electron temperature anisotropy in the polar wind
TL;DR: In this article, the steady state flow of a fully ionized H(+)-O(+)-electron plasma along geomagnetic field lines in the high-latitude topside ionosphere is investigated theoretically, with emphasis on the electron temperature anisotropy and heat flow in the polar wind.
Journal ArticleDOI
Proton temperature anisotropy in the polar wind
TL;DR: The steady state flow of a fully ionized H(+)-O(+) electron plasma along geomagnetic field lines in the high-latitude topside ionosphere is studied in this paper.
Behavior of Ionized Plasma in the High Latitude Topside Ionosphere.
TL;DR: In this article, the steady state behavior of a fully ionized plasma (H+, O+ and the electrons) encompassing the geomagnetic field lines was studied, based on the 16-moment system of transport equations.
References
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Book
Introduction to matrix computations
TL;DR: Rounding-Error Analysis of Solution of Triangular Systems and of Gaussian Elimination.
Journal ArticleDOI
A User’s View of Solving Stiff Ordinary Differential Equations
Lawrence F. Shampine,C. W. Gear +1 more
TL;DR: This paper aims to assist the person who needs to solve stiff ordinary differential equations by identifying the problem area and the basic difficulty and describing the characteristics shared by methods for the numerical solution of stiff problems.
Journal ArticleDOI
Problems with Different Time Scales for Ordinary Differential Equations
TL;DR: In this paper, the authors consider a stiff nonlinear system and assume that the large eigenvalues of the system are purely imaginary, and conditions are given that the system has smooth solutions in long time intervals.
Journal ArticleDOI
Comparison of solutions to the thirteen-moment and standard transport equations for low speed thermal proton flows
TL;DR: In this article, the authors compared the 13-moment system of transport equations with those obtained from the standard collision-dominated transport equations for conditions corresponding to low speed thermal proton flow in the topside ionosphere in the vicinity of the plasmapause.
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A User’s View of Solving Stiff Ordinary Differential Equations
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