The piecewise-linear predictor-corrector code - A Lagrangian-remap method for astrophysical flows

1993 ◽  
Vol 88 ◽  
pp. 569 ◽  
Author(s):  
Eric A. Lufkin ◽  
John F. Hawley
Keyword(s):  
Piecewise Linear ◽  
Linear Predictor ◽  
Astrophysical Flows ◽  
Predictor Corrector

scholarly journals Analytical Predictor-Corrector Guidance Algorithm Based on Drag Modulation Flight Control System for Mars Aerocapture

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Yu-ming Peng ◽  
Bo Xu ◽  
Bao-dong Fang ◽  
Han-lun Lei
Keyword(s):  
Control System ◽  
Flight Control ◽  
Large Scale ◽  
Piecewise Linear ◽  
Scale Space ◽  
Flight Control System ◽  
Initial State ◽  
Aerodynamic Parameter ◽  
Guidance Algorithm ◽  
Predictor Corrector

Aerocapture is one of the essential technologies for future large-scale space exploration missions, as it can significantly reduce the Δv and fuel requirement. The performance and robustness of two different aerocapture control methods are analyzed around Mars exploration, and then an analytic predictor-corrector guidance algorithm for drag modulation flight control system is proposed. A piecewise linear function between velocity and flight path angle is established by appropriate approximations and assumptions, and then the state at atmosphere interface can be predicted by an analytical method; therefore, aerocapture guidance can be realized by feedback control. Numerical simulation is used to evaluate performance and robustness of the algorithm. The simulation results show that the guidance algorithm is accurate and robust, which can effectively overcome the influence of atmospheric density error, aerodynamic parameter error, and initial state uncertainty.

scholarly journals Birth weight threshold for identifying piglets at risk for preweaning mortality

2019 ◽  
Vol 3 (2) ◽  
pp. 633-640 ◽  
Author(s):  
Julie A Feldpausch ◽  
Jan Jourquin ◽  
Jon R Bergstrom ◽  
Jason L Bargen ◽  
Courtney D Bokenkroger ◽  
...  
Keyword(s):  
Birth Weight ◽  
Survival Data ◽  
Change Point ◽  
Piecewise Linear ◽  
Random Effect ◽  
Threshold Value ◽  
Curvilinear Relationship ◽  
Data Set ◽  
Linear Predictor ◽  
Increased Risk

Abstract Several studies have suggested there is a critical relationship between piglet birth weight and preweaning mortality. Thus, the objective of the current work was to identify a birth weight threshold value for preweaning mortality. Birth weight and survival data from two studies involving a combined total of 4,068 piglets from 394 litters on four commercial farms (three European, one U.S.) were compiled for a pooled, multistudy analysis. Overall preweaning mortality across the two studies was 12.2%. Key variables used in the analysis were piglet birth weight (measured within 24 h of birth) and corresponding survival outcome (dead or live) by weaning at 3–4 wk of age. A mixed effects logistic regression model was fit to estimate the relationship between preweaning mortality and birth weight. A random effect of study was included to account for overall differences in mortality between the two studies. A piecewise linear predictor was selected to best represent the drastic decrease in preweaning mortality found as birth weight increased in the range of 0.5–1.0 kg and the less extreme change in weight above 1.0 kg. The change point of the birth weight and preweaning mortality model was determined by comparing model fit based on maximizing the likelihood over the interval ranging from 0.5 to 2.3 kg birth weight. Results from the analysis showed a curvilinear relationship between birth weight and preweaning mortality where the birth weight change point value or threshold value was 1.11 kg. In the combined data set, 15.2% of pigs had birth weights ≤1.11 kg. This subpopulation of pigs had a 34.4% preweaning mortality rate and represented 43% of total preweaning mortalities. These findings imply interventions targeted at reducing the incidence of piglets with birth weights ≤1.11 kg have potential to improve piglet survivability. Additional research is needed to validate 1.11 kg as the birth weight threshold for increased risk of preweaning mortality.

scholarly journals Modified Predictor-Corrector WAF Method for the Shallow Water Equations with Source Terms

2011 ◽  
Vol 2011 ◽  
pp. 1-17 ◽  
Author(s):  
Montri Maleewong
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Numerical Solutions ◽  
Piecewise Linear ◽  
Weighted Average ◽  
Test Cases ◽  
Half Time ◽  
Source Terms ◽  
Time Step ◽  
Predictor Corrector

A modified predictor-corrector scheme combining with the depth gradient method (DGM) and the weighted average flux (WAF) method has been presented to solve the one-dimensional shallow water equations with source terms. Approximate solutions in the predictor step are obtained by the DGM with piecewise-linear reconstructions in each cell volume. The source terms can then be calculated directly by these predicted values at the corresponding half-time step. In the corrector step, the TVD version of the WAF method is applied to calculate the numerical fluxes at the same half-time step for each cell face. The accuracy of numerical solutions is shown by applying the method to solve various test cases in both steady and unsteady problems with and without source terms. It shows that the numerical results are in good agreement with the existing analytical solutions as well as experimental data in some test cases.

Continuation and path following

Acta Numerica ◽  
1993 ◽  
Vol 2 ◽  
pp. 1-64 ◽  
Author(s):  
Eugene L. Allgower ◽  
Kurt Georg
Keyword(s):  
Eigenvalue Problems ◽  
Piecewise Linear ◽  
Path Following ◽  
Parametric Programming ◽  
Polynomial Systems ◽  
Nonlinear Eigenvalue Problems ◽  
Interior Methods ◽  
Main Ideas ◽  
New Applications ◽  
Predictor Corrector

The main ideas of path following by predictor–corrector and piecewise-linear methods, and their application in the direction of homotopy methods and nonlinear eigenvalue problems are reviewed. Further new applications to areas such as polynomial systems of equations, linear eigenvalue problems, interior methods for linear programming, parametric programming and complex bifurcation are surveyed. Complexity issues and available software are also discussed.

scholarly journals Solving Fractional Dynamical System with Freeplay by Combining Memory-Free Approach and Precise Integration Method

2016 ◽  
Vol 2016 ◽  
pp. 1-7
Author(s):  
Q. X. Liu ◽  
X. S. He ◽  
J. K. Liu ◽  
Y. M. Chen ◽  
L. C. Huang
Keyword(s):  
Integration Method ◽  
Piecewise Linear ◽  
Harmonic Excitation ◽  
Precise Integration ◽  
Linear Ordinary Differential Equations ◽  
First Order ◽  
Precise Integration Method ◽  
Runge Kutta Method ◽  
Predictor Corrector ◽  
Fractional Dynamical System

The Yuan-Agrawal (YA) memory-free approach is employed to study fractional dynamical systems with freeplay nonlinearities subjected to a harmonic excitation, by combining it with the precise integration method (PIM). By the YA method, the original equations are transformed into a set of first-order piecewise-linear ordinary differential equations (ODEs). These ODEs are further separated as three linear inhomogeneous subsystems, which are solved by PIM together with a predictor-corrector process. Numerical examples show that the results by the presented method agree well with the solutions obtained by the Runge-Kutta method and a modified fractional predictor-corrector algorithm. More importantly, the presented method has higher computational efficiency.

Symmetric Multistep Methods Revisited: II. Numerical Experiments

1999 ◽  
Vol 173 ◽  
pp. 309-314 ◽  
Author(s):  
T. Fukushima
Keyword(s):  
Multistep Methods ◽  
Computational Time ◽  
Integration Time ◽  
Implicit Methods ◽  
Symmetric Methods ◽  
Celestial Bodies ◽  
The Stability ◽  
Predictor Corrector ◽  
Symmetric Multistep Methods ◽  
Integration Errors

AbstractBy using the stability condition and general formulas developed by Fukushima (1998 = Paper I) we discovered that, just as in the case of the explicit symmetric multistep methods (Quinlan and Tremaine, 1990), when integrating orbital motions of celestial bodies, the implicit symmetric multistep methods used in the predictor-corrector manner lead to integration errors in position which grow linearly with the integration time if the stepsizes adopted are sufficiently small and if the number of corrections is sufficiently large, say two or three. We confirmed also that the symmetric methods (explicit or implicit) would produce the stepsize-dependent instabilities/resonances, which was discovered by A. Toomre in 1991 and confirmed by G.D. Quinlan for some high order explicit methods. Although the implicit methods require twice or more computational time for the same stepsize than the explicit symmetric ones do, they seem to be preferable since they reduce these undesirable features significantly.

Chaos in a manifold piecewise linear system

1981 ◽  
Vol 64 (10) ◽  
pp. 9-17 ◽  
Author(s):  
Toshimichi Saito ◽  
Hiroichi Fujita
Keyword(s):  
Linear System ◽  
Piecewise Linear ◽  
Piecewise Linear System
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