Global error estimation for explicit general linear methods

2021 ◽  
Author(s):  
Ali Abdi ◽  
Gholamreza Hojjati ◽  
Giuseppe Izzo ◽  
Zdzislaw Jackiewicz
Keyword(s):  
Error Estimation ◽  
General Linear Methods ◽  
Global Error ◽  
General Linear ◽  
Global Error Estimation

scholarly journals Global error estimation with runge-kutta triples

1989 ◽  
Vol 18 (9) ◽  
pp. 835-846 ◽  
Author(s):  
J.R. Dormand ◽  
M.A. Lockyer ◽  
N.E. McGorrigan ◽  
P.J. Prince
Keyword(s):  
Error Estimation ◽  
Global Error ◽  
Runge Kutta ◽  
Global Error Estimation

Error Estimation for a Economic Equilibrium Modeling

2011 ◽  
Vol 267 ◽  
pp. 350-355
Author(s):  
Lei Wang
Keyword(s):  
Error Estimation ◽  
Linear Complementarity Problem ◽  
Complementarity Problem ◽  
Linear Complementarity ◽  
Economic Equilibrium ◽  
Global Error ◽  
Equilibrium Modeling ◽  
Generalized Linear Complementarity Problem ◽  
Global Error Estimation

In this paper, the global error estimation for the generalized linear complementarity problem in economic equilibrium modeling(GLCP) is established. The result obtained in this paper can be viewed as extensions of previously known results.

Efficient Numerical Shadowing Global Error Estimation for High Dimensional Dissipative Systems

2004 ◽  
Vol 4 (2) ◽  
Author(s):  
Jon Collis ◽  
Erik S. Van Vleck
Keyword(s):  
Error Estimation ◽  
Initial Conditions ◽  
Efficient Estimation ◽  
Global Error ◽  
Dissipative Systems ◽  
High Dimensional ◽  
Initial Value ◽  
Small Perturbations ◽  
One Step ◽  
Global Error Estimation

AbstractShadowing is a means of characterizing global errors in the numerical solution of initial value differential equations by allowing for small perturbations in the initial conditions. The method presented in this paper provides a technique for efficient estimation of the shadowing global error for systems that have a large number of exponentially decaying modes. The method is formulated for one-step methods and is applied to the spatial discretization of some dissipative PDEs.

scholarly journals Saul’yev and Group Explicit Methods

2019 ◽  
pp. 19
Author(s):  
Ole Østerby
Keyword(s):  
Error Estimation ◽  
Parabolic Equations ◽  
Parallel Computers ◽  
Global Error ◽  
Explicit Methods ◽  
Step Size ◽  
Time Step ◽  
Space Step ◽  
Linear Problems ◽  
Global Error Estimation

The Saul’yev methods for parabolic equations are implicit in form, but can be solved explicitly and are therefore interesting in connection with non-linear problems. Abdullah’s Group Explicit methods are parallel in nature and therefore interesting when using parallel computers. The  main objective of this paper is to study the accuracy of these methods. Using global error estimation we show that for all these methods the time step must be bounded by the square of the space step size to ensure a global error which can be estimated. As a curiosity we show that the two original Saul’yev methods in fact solve two different differential equations.  

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