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

Author(s):  
V. Kazemi-Kamyab* ◽  
A.H. van Zuijlen ◽  
H. Bijl
Author(s):  
M Rezaiee-Pajand ◽  
S R Sarafrazi

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.


Author(s):  
Murat Demiral

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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