scholarly journals ON THE STABILITY OF LOOSE AND STRONG PARTITIONED ALGORITHMS FOR THERMAL COUPLING OF DOMAINS USING HIGHER ORDER IMPLICIT TIME INTEGRATION SCHEMES

2014 ◽  
Author(s):  
V. Kazemi-Kamyab* ◽  
A.H. van Zuijlen ◽  
H. Bijl
Keyword(s):  
Time Integration ◽  
Higher Order ◽  
Implicit Time ◽  
Thermal Coupling ◽  
Integration Schemes ◽  
Implicit Time Integration ◽  
Time Integration Schemes ◽  
The Stability

A Mixed and Multi-Step Higher-Order Implicit Time Integration Family

2010 ◽  
Vol 224 (10) ◽  
pp. 2097-2108 ◽  
Author(s):  
M Rezaiee-Pajand ◽  
S R Sarafrazi
Keyword(s):  
Time Integration ◽  
Higher Order ◽  
Trapezoidal Rule ◽  
Implicit Time ◽  
Benchmark Problems ◽  
Integration Schemes ◽  
Implicit Time Integration ◽  
Time Integration Schemes ◽  
The Stability ◽  
Stability And Accuracy

This article develops a new time integration family for second-order dynamic equations. A combination of the trapezoidal rule and higher-order Newton backward extrapolation functions are utilized in the formulation. Five members of the suggested family are extensively studied in this article. Most members of the presented time integration family are new. The stability and accuracy of the proposed time integration schemes are investigated by solving some benchmark problems. Numerical results are checked and compared with well-known strategies. The findings of the article show the efficiency, accuracy and robustness of the suggested techniques.

Comparison of Implicit Time Integration Schemes for Nonlinear Dynamic Problems

2010 ◽  
Author(s):  
Murat Demiral
Keyword(s):  
Dynamic Equilibrium ◽  
Time Integration ◽  
Nonlinear Problems ◽  
Implicit Time ◽  
Implicit Methods ◽  
Equilibrium Equations ◽  
Integration Schemes ◽  
Implicit Time Integration ◽  
Time Integration Schemes ◽  
The Stability

Implicit time integration schemes are used to obtain stable and accurate transient solutions of nonlinear problems. Methods that are unconditionally stable in linear analysis are sometimes observed to have convergence problems as in the case of solutions obtained with a trapezoidal method. On the other hand, a composite time integration method employing a trapezoidal rule and a three-point backward rule sequentially in two half steps can be used to obtain accurate results and enhance the stability of the system by means of a numerical damping introduced in the formulation. To have a better understanding of the differences in the numerical implementation of the algorithms of these two methods, a mathematical analysis of dynamic equilibrium equations is performed. Several practical problems are studied to compare the implicit methods.

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