A class of parallel Rosenbrock methods for differential algebraic equations are presented in this paper. The local truncation errors are defined and the order conditions are established by using the DA-trees and DA-se...A class of parallel Rosenbrock methods for differential algebraic equations are presented in this paper. The local truncation errors are defined and the order conditions are established by using the DA-trees and DA-series. The paper also deals with the convergence of the parallel Rosenbrock methods for h -> 0 and states the bounds for the global errors of the methods. Some particular methods are obtained by solving the order equations and a numerical example is given, from which the theoretical orders are actually observed.展开更多
The stability analysis of the Rosenbrock method for the numerical solutions of system of delay differential equations was studied. The stability behavior of Rosenbrock method was analyzed for the solutions of linear t...The stability analysis of the Rosenbrock method for the numerical solutions of system of delay differential equations was studied. The stability behavior of Rosenbrock method was analyzed for the solutions of linear test equation. The result that the Rosenbrock method is GP-stable if and only if it is A-stable is obtained.展开更多
In this paper parallel Rosenbrock methods in real-time simulation are presented on parallel computers. Their construction, their convergence and their numerical stability are studied, and the numerical simulation expe...In this paper parallel Rosenbrock methods in real-time simulation are presented on parallel computers. Their construction, their convergence and their numerical stability are studied, and the numerical simulation experiments are conducted on a personal computer and a parallel computer respectively. [ABSTRACT FROM AUTHOR]展开更多
Presents a class of modified parallel Rosenbrock methods (MPROW) which possesses more free parameters to improve further the various properties of the methods and will be similarly written as MPROW. Information on par...Presents a class of modified parallel Rosenbrock methods (MPROW) which possesses more free parameters to improve further the various properties of the methods and will be similarly written as MPROW. Information on parallel Rosenbrock methods; Convergence and stability analysis; Discussion on two-stage third-order methods.展开更多
基金the National Natural Science Foundation of China (No. 19871080)
文摘A class of parallel Rosenbrock methods for differential algebraic equations are presented in this paper. The local truncation errors are defined and the order conditions are established by using the DA-trees and DA-series. The paper also deals with the convergence of the parallel Rosenbrock methods for h -> 0 and states the bounds for the global errors of the methods. Some particular methods are obtained by solving the order equations and a numerical example is given, from which the theoretical orders are actually observed.
文摘The stability analysis of the Rosenbrock method for the numerical solutions of system of delay differential equations was studied. The stability behavior of Rosenbrock method was analyzed for the solutions of linear test equation. The result that the Rosenbrock method is GP-stable if and only if it is A-stable is obtained.
文摘In this paper parallel Rosenbrock methods in real-time simulation are presented on parallel computers. Their construction, their convergence and their numerical stability are studied, and the numerical simulation experiments are conducted on a personal computer and a parallel computer respectively. [ABSTRACT FROM AUTHOR]
文摘Presents a class of modified parallel Rosenbrock methods (MPROW) which possesses more free parameters to improve further the various properties of the methods and will be similarly written as MPROW. Information on parallel Rosenbrock methods; Convergence and stability analysis; Discussion on two-stage third-order methods.
